An Economic Theory of War∗

Nuno Monteiro† and Alexandre Debs‡

September 18, 2015

Abstract

When does war occur for economic reasons? The aggregate wealth two states can

divide depends on how efficiently each of them is able to invest its own resources. When

one state is able to set the terms on which another accesses resources it needs in order to

grow efficiently, an economic hold-up problem may result, making peace inefficient. War

happens when fighting is expected to eliminate this hold-up problem, leading to faster

growth. This explanation for war results from a stronger state’s inability to commit

to grant weaker states generous terms of access to resources vital to their economic

growth. This mechanism accounts for wars launched by weaker states, even if they are

rising, and helps account for how the current global free-trade regime promotes peace.

We illustrate our theory by analyzing the economic roots of World War II in Europe

and the Pacific.

∗The authors contributed equally to this article. For comments and suggestions, we thank Stephen Brooks,Dale Copeland, Christina Davis, Joanne Gowa, Matthew Kocher, Catherine Langlois, Jeffrey Legro, JackLevy, Paul Rubinson, Bruce Russett, John Schuessler, Duncan Snidal, Milan Svolik; seminar participants atDartmouth, Georgetown, the Institute for Advanced Study in Toulouse, NYU-Abu Dhabi, Maryland, Oxford,Pennsylvania, Rice, and Columbia; participants in the 2015 Empirical Implications of Bargaining Theoryconference at Princeton; and the audience at the 2013 APSA meeting. For excellent research assistance, wethank Demi Horvat, Yedida Kanfer, Tess McCann, Chad Peltier, and William Schreiber.†Dept. of Political Science, Yale University. Email: nuno.monteiro@yale.edu‡Dept. of Political Science, Yale University. Email: alexandre.debs@yale.edu

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1 Introduction

When does war happen for economic reasons? Existing work focuses on the potential that

trade and economic growth have to generate conflict. Before trade and growth take place,

however, states must allocate resources to economic production. We show how international

constraints on states’ ability to invest their resources efficiently can lead to war.

Powerful states can condition others’ access to resources they need in order to invest their

own resource endowments efficiently, hamstringing their growth. When this economic hold-

up problem is sufficiently severe, war may be rational for the weaker state. Although fighting

is costly and the state’s relative weakness makes victory less likely, winning would allow it

to invest its resources efficiently, maximizing growth. War happens when it is expected to

produce a gain in economic efficiency large enough to make the expected outcome of fighting

better than the continuation of an inefficient peace. War is rational not depending on whether

a state is rising or declining, but on whether fighting is expected to result in faster growth.

Our argument highlights how the postwar global free-trade regime supports peace by

undermining an incentive for war: the need to alleviate economic hold-up problems (Carnegie,

2014) resulting from powerful states’ ability to set the terms on which weak states can access

resources they need for efficient growth. In the highly institutionalized contemporary global

trade setting, even powerful states would pay a heavy price for attempting to deny weaker

states access to vital economic resources (Ikenberry, 2001; Lake, 2009; Milner, 2010). This

allows weak states to invest their resource endowments efficiently, eliminating incentives to

fight in order to boost growth.

Our argument also sheds light on how power transitions lead to conflict. Existing schol-

arship claims that it is not rational for a weaker rising state to resort to arms. Only powerful

states start wars, either because they anticipate their own decline (Powell, 1999; Copeland,

2000; Powell, 2006; Copeland, 2014) or because, having risen in power, they are now dissat-

isfied with the status quo (Organski and Kugler, 1980; Gilpin, 1981). If a state is sufficiently

strong, however, it can extract favorable terms peacefully, eliminating the need to fight unless2

it expects steep decline. Weaker states are the ones likely to face less favorable conditions,

giving them incentives to fight for better terms. We account for why a weaker rising state

may rationally launch a war – even if the continuation of peace would allow its relative power

to rise.

In our theory, war is caused by a previously unspecified commitment problem stemming

from a powerful state’s difficulty in committing not to exploit its dominant international

economic position. This commitment problem leads to war in the absence of information

problems even when a bargain is feasible. Canonical perfect information models (Fearon,

1995; Powell, 2006) produce war only when a state’s minimum demand is unfeasible, i.e.,

greater than the total object of bargaining. Our model produces war when both demands

are feasible but incompatible, i.e., when one state’s minimum demand exceeds the other’s

maximum offer. When future surpluses depend on investment decisions, a state might de-

mand more to avoid fighting than another is willing to offer. Specifically, when economic

surpluses are expected to grow faster after war than if an inefficient peace were maintained,

war is expected to be less costly than peace, becoming efficient.

The following section discusses the literature on economic growth and war. We then

introduce our argument and formalize it in a game-theoretic model. Next, we show how our

theory is compatible with the historical record and use it to highlight the economic dimension

of the causes of World War II [WWII], which was launched by comparatively weaker states –

Germany and Japan. Proofs of the formal results are in the Appendix (to be placed online).

2 The International Environment, Growth, and War

According to a common argument, trade increases the opportunity cost of war or otherwise

obviates the need for territorial conquest, supporting peace (Polachek, 1980; Rosecrance,

1986; Crescenzi, 2003; Martin, Mayer and Thoenig, 2008). While intuitive, this idea has

been questioned using three lines of criticism. First, this argument glosses over complex

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strategic effects. As the opportunity cost of war increases, a state may be less willing to

declare war. Anticipating this, another state may be more willing to escalate a conflict. As

a result, the net effect of trade on the likelihood of war may be indeterminate (Morrow,

1999; Gartzke, Li and Boehmer, 2001). Second, the pacifying effect of trade depends not on

its levels but on trade policy. To promote peace, trade must result from pro-trade policies

rather than technological advances (McDonald, 2009). Finally, economic exchanges reinforce

peace only when expectations of future trade do not decrease (Copeland, 2014). A state that

is highly reliant on trade may worry that being “cut off” by its partner(s) would result in

economic decline, leading it to strike preventively (Copeland, 2014).

By focusing on the role of expectations about future trade, Copeland’s argument sheds

new light on how economic interaction can produce conflict. Yet, it does not provide a

coherent theory of whence shifts in trade expectations originate (Copeland, 2014, 43-7).

While explaining the timing of war – conflict breaks out when a state’s expectations of

future trade decline – Copeland’s theory does not account for what causes war: why do trade

expectations change? Furthermore, since war always involves an opportunity cost in trade,

why is a state with declining trade expectations unable to negotiate a peaceful settlement?

Preventive dynamics generated by expected changes in economic power also play a promi-

nent role in arguments about how power transitions cause war. In the canonical view, the

“source of war is to be found in the differences in size and rates of growth of the members

of the international system” (Organski and Kugler, 1980, 20). While some scholars believe

that war is rational only for a declining state (Copeland, 2000), others argue that war makes

sense for rising states but only after matching their opponents’s power (Organski and Kugler,

1980; Gilpin, 1981).

Rationalist explanations for war often also focus on economic power trajectories (Fearon,

1995; Powell, 1999, 2006). A rising state is unable to commit to maintaining current bargains

in the future, providing declining states with incentives to strike preventively in order to

prolong a beneficial status quo. This formal literature accounts for why states choose war

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instead of a peaceful revision of the status quo. Like the power transition literature, however,

rationalist accounts also predict that only declining states will go to war.

In sum, we have no arguments accounting for wars launched by relatively weak rising

states. Yet, important wars were initiated by weak rising states. Such was the case with

WWII, started in Europe and Asia by, respectively, Germany and Japan. These two states,

which behaved in a highly bellicose manner during the first half of the twentieth century, were

at the center of what Paul Kennedy labeled, the “crisis of the ‘middle powers’” (Kennedy,

1989, 249-447). The rise of Russia and the United States as continental powers that had

access to resources and markets far greater than those controlled by any of their smaller peer

competitors placed these ‘middle powers’ in a tough predicament: how to guarantee access

to the resources necessary to compete with the American and Soviet juggernauts? Germany

and Japan ultimately decided that war was the best way to attempt to break out of this

constraint, despite their relative economic rise in the years leading up to the war.1

These limitations of existing work on the economic causes of war result from an incom-

plete conceptualization of economic interactions. Most existing work assumes that the object

of states’ bargaining has a value that is fixed and independent of their action (Fearon, 1995;

Powell, 2006).2 But this assumption is not appropriate when states negotiate over the distri-

bution of aggregate wealth. States determine their aggregate wealth by choosing economic

policies and investing their resource endowments. The set of possible policies includes eco-

nomic interaction – through flows of economic resources as well as finished products and

services – which may increase their aggregate wealth. Understanding the economic causes

of war requires a richer conceptualization of peace, incorporating the role of resource access

and economic investments.

1Furthermore, states are usually rising vis-a-vis some peers and declining vis-a-vis others, making itdifficult to evaluate existing arguments in wars with more than two states, since they depend on relativepower trajectories.

2A partial exception to this feature is the literature on bargaining over objects that affect future bargaining(Fearon, 1995, 1996; Powell, 2013). Yet, none of these works makes the value of the object over which statesbargain endogenous to state decisions.

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3 An Economic Theory of War

Our theory focuses on how international economic interactions may constrain the efficiency

with which states can invest their resources and grow efficiently. This requires us to make

economic growth the endogenous product of states’ investment decisions. Countries rarely

possess all resources necessary for efficient economic growth and often procure them inter-

nationally. The more powerful a state is, the greater the influence it will have on global

resource markets, impacting others’ terms of access to them, for example by manipulating

prices, imposing sanctions, or adopting export controls (Gowa and Mansfield, 2004). We the-

orize a situation in which a weaker challenger is dependent on a stronger state, the hegemon,

for access to resources it needs in order to convert its own resource endowment into output

efficiently, maximizing growth. We define dependency as a situation in which the hegemon

has the ability to set the cost the weaker challenger pays for resources it needs.3

By endogenizing growth and considering the possibility that a weaker state’s access to

resources be constrained by a stronger state, we uncover a new mechanism connecting eco-

nomic interaction and war. In the anarchic international environment, an economic hegemon

faces a commitment problem: it cannot commit to refrain from using its economic power to

extract the best possible terms it can from weaker states. But if the hegemon uses its power

to appropriate a disproportionate share of the gains in its interactions with a challenger, the

challenger will react by under-investing its available resource endowment in tradeable goods

and services, thereby failing to maximize its own economic growth. An efficient investment of

resources could maximize the benefits of peace – i.e., the total value of the economic surplus

– but the challenger might reap a share of these benefits that is insufficient to justify this

investment. Consequently, when the hegemon constrains the challenger’s ability to maximize

its own economic growth, the challenger may prefer to attempt to overturn the status quo

3We use the labels ‘hegemon’ and ‘challenger’ because our empirical focus is on great-power dynamics.Strictly, what defines the hegemon is its ability to constrain the challenger’s access to resources it needs foreconomic growth. Conversely, the challenger is defined by its dependency on the hegemon to access theseresources. Therefore, the theory can also account for relations between any other dyads of states (er evensub-state actors) as long as these conditions hold.

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by military means.4

Incorporating these power imbalances at play in the international political economy –

and recognizing the hegemon’s commitment problem described above – allows us to build an

economic theory of war. Other papers have argued that peace can be inefficient (Powell, 1999,

2006; Fearon, 2008; Coe, 2011; Debs and Monteiro, 2014). Yet no existing scholarship has

endogenized the value of the aggregate wealth states can divide – the ‘pie’ – while highlighting

this commitment problem.

The hegemon is more likely to impose terms that preclude the challenger’s efficient growth

when two conditions are present. First, the challenger’s growth presents negative externalities

for the hegemon’s security.5 Access to a key economic resource might allow the challenger

to grow and threaten the hegemon’s security or that of its allies. Second, the cost the

hegemon would pay for constraining the challenger’s growth is low. Such is the case when

international economic interaction is weakly institutionalized, allowing the hegemon to single

out the challenger’s resource access; and when the challenger does not possess a large sphere

of influence, which would limit the ability of the hegemon to constrain its growth.

When the hegemon constrains the challenger’s economic growth, the challenger will be

tempted to fight. All other things equal, the higher is the growth inefficiency imposed by the

hegemon on weaker states, the higher is the likelihood of conflict. This mechanism highlights

how certain features of the international systems – namely, weakly institutionalized trade,

power imbalances that favor an economic hegemon, and challengers that do not possess well

established spheres of economic influence – increase the value of conquering resource-rich

territory, making conflict more likely.

Although it is unclear whether the opportunity costs of trade, as delineated in the extant

literature, are sufficient to avoid war, our argument highlights a different mechanism through

which the post-WWII global economic regime of open trade supports peace. An open in-

4For a recent application in the international political economy literature, see Carnegie (2014).5On security externalities associated with trade, see Gowa and Mansfield (1993); Gowa (1994). Other

factors, such as market and economic structures, may contribute to variation in the extent to which thehegemon is able to constrain the challenger’s ability to invest its economic resources efficiently.

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ternational economy supported by institutions that make it more costly for powerful states

to exploit their weaker peers is a force for peace (Gowa, 1994; Mansfield, 1994; Goldstein

and Gowa, 2002; Milner, 2005; Davis and Wilf, 2014). The contemporary free-trade struc-

ture of the global economy alleviates economic hold-up problems that might affect weaker

states if their access to resources were to be controlled by powerful states, as was the case in

earlier historical periods. Today, given the highly institutionalized character of international

trade, the costs of excluding a state from accessing resources it needs for growth would be

particularly high, even for the the United States, which possesses the largest economy in the

world.

This logic has consequences for the relationship between power shifts and war. Whereas

existing literature focuses on relative power trajectories – investigating whether it is rising

or declining states that launch wars – our argument highlights a different strategic calculus.

Challengers decide whether to resort to arms by comparing the expected outcome of peace

and war, regardless of whether they are rising or declining. The odds of conflict depend

on the magnitude of the economic inefficiency that the hegemon imposes on the challenger.

Whenever this inefficiency is greater than the cost of war, conflict is likely to ensue regardless

of the power trajectory of the challenger relative to the hegemon. The weaker the challenger,

the greater this inefficiency. Therefore, war happens only when the challenger’s probability

of victory is not too high – i.e., when the challenger is not too strong.

Certainly, a weak challenger is less likely to prevail in war. By the same token, however,

a weak challenger cannot use the threat of war effectively to obtain favorable terms of peace.

The higher is the probability that the challenger wins the war, the greater the threat it

represents to the hegemon, who will offer it more favorable terms peacefully. Thus, the

higher the probability that the challenger wins the war, the more efficiently it will be able

to invest in economic output, and the lower the inefficiency of peace. It is relatively weak

states that may need to fight in order to obtain favorable terms of economic interaction.

Only relatively weak challengers are likely to launch wars for economic reasons.6

6Conversely, the hegemon may want to launch a war so as to gain control over the weak challenger’s8

Conflict may be rational for the challenger even if peace would allow for its power to rise

in relative terms, as long as war is expected to accelerate this rise. Whenever the challenger

expects fighting to result in less inefficiency than the maintenance of peace, it will declare

war. If the challenger’s power is rising, it will be able to extract better terms from the

hegemon in the future, resulting in more efficient future investments in economic growth.

Therefore, there is no case in which war would be rational after the challenger has greater

relative power but does not presently make sense. Conflict will always occur before, not after,

a challenger’s rise in power. This explains why even weaker rising challengers may rationally

go to war.7

Our argument also has implications for rationalist explanations for war. In the standard

framework, war between rational states under complete information results from a military

commitment problem. Unable to commit not to use its military power in the future, a rising

state may induce a declining state to declare war preventively (Fearon, 1995; Powell, 2006).

In this framework, war happens because when the declining state anticipates a sufficently

large and rapid adverse shift in relative power, the minimum demand it is willing to accept

is not feasible – i.e. it is greater than the entire object in dispute, or “pie.” Under the

constraints of a fixed pie, and given that war is costly, a bargaining range always exists – i.e.

the minimum demand of a rising state is always less than the maximum offer of a declining

state. The rising state always gains from peace, which allows the balance of power to shift

in its favor.

But, as we have seen, the assumption that the pie over which states bargain is fixed does

not capture essential features of states’ economic interaction, including their decisions to

allocate resources to producing tradeable goods and services, which determines the value of

resources, which it can then invest more efficiently. This dynamic may help account for colonial conquestwars and for their demise in the post-WWII era of relatively free resource access. We reserve this aspect ofour argument for future research.

7This allows us, in contrast with Copeland (2014)’s trade expectations theory, to offer predictions aboutthe conditions under which economic dependency is more likely to result in conflict. (See proposition 1below.) Copeland (2014) argues that war happens when expectations about economic interaction shift. Ourargument is about why particular expectations about economic interaction – i.e. expectations about howefficiently the challenger will be able to grow – emerge.

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the surplus to be divided. When we allow the value of the object over which states bargain

to vary according to the states’ decisions to invest in a tradeable surplus, however, the

bargaining range may be eliminated. When the cost the challenger has to pay for resources

essential to its economic growth is sufficiently high, and when the challenger expects war to

eliminate this inefficiency, the minimum demand it would accept may become higher than

the maximum offer the hegemon is willing to make. When this is the case, the two states’

demands are no longer compatible, the bargaining range is eliminated, and war is the rational

course of action even for a challenger that is weak and rising.

4 The Model

4.1 Baseline Framework

We model a political economy between two states. Call the first state H for ‘hegemon’ and

the second state C for ‘challenger’. The two states bargain over the control of economic

resources, or ‘butter.’ If peace prevails, C chooses the investment in butter. H, which

dominates the international political economy, may intervene in world markets to capture

part of the surplus created by C.

Let b be C’s investment in butter. An investment in butter costs kb > 0 per unit and

produces a surplus of value S(b)(1 + σ). S(b) is the economic value of the surplus. It is

increasing and concave in b, and equal to 0 when there is no investment, with the marginal

return of an investment arbitrarily large at b = 0, i.e. S ′(.) > 0, S ′′(.) < 0, S(0) = 0, and

limb→0S′(b) = ∞. σ is the value of the externalities created by the surplus. For example,

the resources that C obtains by selling its surplus may improve its strategic position against

third parties. For simplicity, assume that σ takes one of two values, σ ∈ {σ, σ}, where σ = 0

and σ is ‘large’ (proofs will explain the minimal bounds for σ). The probability that σ takes a

value of σ is ρσ. As a benchmark, write be for the efficient investment in butter, i.e. the value

of b which solves max− kbb+ S(b)(1 + σ). Given that the marginal benefit of investment at

10

b = 0 is arbitrarily large, be is strictly positive and characterized by the following first-order

condition: S ′(be) = kb1+σ

.

After C invests in creating a surplus, it attempts to sell it on the international market.

Under conditions of ‘free market,’ C receives the total value of the surplus, S(b)(1+σ). Under

a ‘captured market,’ H uses its influence over the international market to dictate the share

of the surplus that C obtains. Specifically, H makes a take-it-or-leave-it offer to C, choosing

the value z that C obtains, z ∈ [0, S(b)(1 + σ)], and keeping the difference S(b)(1 + σ)− z.

If C accepts the offer, it is implemented. If C rejects the offer, a war ensues and the winner

of the war obtains the total value of the surplus.8 For simplicity, assume that if no surplus

is created, the game ends.9

A war is won by C with probability p(κ), where κ is a measure of its capabilities. Let

p(κ) be strictly between 0 and 1, increasing in capabilities at a decreasing rate, i.e. p(.) ∈

[pmin, pmax] ⊂ (0, 1), p′(.) > 0, p′′(.) < 0, and limκ→∞p′(κ) = 0. Following the standard

framework, war is costly (Fearon, 1995). Let ci be the cost paid by country i if a war is

fought, where i ∈ {C,H}. We assume that ci > 0, ∀i ∈ {C,H}, and we call cC + cH the cost

of war.

An attempt by H to capture the international market and, with it, part of the surplus

produced by C, entails a cost. Let kc be the cost that H pays for capturing the market.

For simplicity, assume that kc takes one of two values, kc ∈{k, k}

, where k is equal to the

economic value of the surplus, i.e. k = S(b), and k is arbitrarily large. We assume that the

cost H must pay to capture the market is low with a probability that decreases with the

strength of international institutions and the size of C’s sphere of influence. So, for example,

H would pay a lower cost for capturing the market in its interaction with a state C when

their economic interactions are weakly institutionalized and C possesses no formal sphere

of economic influence. Conversely, H would pay a high cost to capture the market when

8We could also let H declare war instead of capturing the market, but the results would hold so we ignorethis possibility.

9In this case, it is difficult to speak of the hegemon capturing the market, since there is nothing to capture.

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interacting with a state C that is a member of multilateral free-trade institutions, such as

the WTO, or that possesses a vast sphere of economic influence, such as the Soviet Union

during the Cold War. Mathematically, the probability that kc takes a value k is ρk(η, θ),

where η ∈ R+ represents the strength of international institutions (greater values correspond

to stronger institutions), θ ∈ R+ represents the size of C’s sphere of influence (greater values

correspond to larger spheres of influence), and ρk(η, θ) is decreasing in both η and θ.

Prior to C’s investment in butter, and the subsequent division of the surplus with H, we

let the two bargain over the control of the resources and choose whether to go to war. H

can demand a transfer T (T ∈ R) from C or decide to declare war. C can decide to accept

or reject H’s demand.

If H and C go to war, call V the victor and L the loser of the war. After the war, V

chooses the level of investment in butter, obtains the full value of the surplus, and wins any

subsequent war fought over the division of the surplus.

To recap, the timing of the game is as follows (for a graphical illustration, see Figure 1):

1. Nature determines the value of the externalities σ and the cost of capturing the market

kc;

2. H demands a transfer T or decides to declare war;

3. C accepts H’s demand of T or declares war.

If peace prevails, the game proceeds as follows:

1. C makes an investment decision b.

2. The surplus S(b) is created. If no surplus is created, the game ends.

3. If a surplus is created, H decides whether to capture the market and, if so, chooses the

offer z to make to C.

4. If a surplus is created and H captured the market, C decides whether to accept H’s

offer z or declare war.12

If the negotiation over T ended in war, then the game proceeds as follows:

1. V makes an investment decision b.

2. The surplus S(b) is created. If no surplus is created, the game ends.

3. If a surplus is created, V decides whether to capture the market and, if so, chooses the

offer z to make to L.

4. If a surplus is created and V captured the market, L decides whether to accept V ’s

offer z or declare war.

—Figure 1 about here.—

Throughout the interaction between C and H, we assume perfect and complete informa-

tion. We solve for a subgame-perfect Nash equilibrium of this game.

4.2 Solution of the Baseline Model

We proceed by backward induction. First consider the case where negotiations over the

transfer T for control of the resources ended in war. By assumption, V would win any

military conflict, so that if V captured the market, it could propose to keep the surplus and

L would have to accept it. However, V would not capture the market, since doing so is costly

and V could obtain the full value of the surplus on the free market. Anticipating that it

obtains the full value of the surplus that it creates, V chooses the efficient level of investment.

In sum:

Lemma 1 After war, V chooses the efficient level of investment, i.e. be such that S ′ (be) =

kb1+σ

; V does not capture the market; if it did, it would offer z = 0 and L would accept any

z ≥ 0. Proof. Straightforward.

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Now consider the case where negotiations over the transfer T for the control of the re-

sources ended peacefully. First assume that H decides to capture the market. C accepts a

division of the surplus if and only if its payoff is at least as high as what it would obtain

by going to war, i.e. if z ≥ p(κ)S(b)(1 + σ) − cC . Similarly, H is willing to make an offer

that is accepted if and only if it procures a payoff at least as high as its payoff from war,

i.e. S(b)(1 + σ)− z ≥ (1− p(κ))S(b)(1 + σ)− cH . Since war is costly, there is a bargaining

range and there are values of z that both states would prefer to war (Fearon, 1995). If H

captures the market, H makes an offer that leaves C indifferent between war and peace, i.e.

z = max {0, p(κ)S(b)(1 + σ)− cC}.

Next we investigate the conditions under which H would capture the market, when there

is a strictly positive surplus. If H does not capture the market, it gets a payoff of zero. If it

captures the market, H pays a cost kc but obtains part of the surplus. Therefore, H captures

the market if and only if kc < min {S(b)(1 + σ), (1− p(κ))S(b)(1 + σ) + cC}. This condition

holds if and only if the cost of capture is low, the value of externalities is high, and such a

value σ is sufficiently high.10 Otherwise, the cost of capture is greater or equal to the total

value of the surplus, which is strictly greater than the concessions that H would extract from

C after capturing the market. In sum, we conclude:

Lemma 2 After peace, there is a value σ′ such that for any σ > σ′, the following holds: H

captures the market if and only if the cost of capture is low (kc = k) and the value of externali-

ties is high (σ = σ). After capturing the market, H offers z = max {0, p(κ)S(b)(1 + σ)− cC},

and C accepts if and only if z ≥ max {0, p(κ)S(b)(1 + σ)− cC}. Proof. Straightforward.

Moving up, we analyze C’s investment decision. When the cost of capture is high or the

value of externalities is low, C expects to obtain the full value of any surplus it creates. In

this case, C chooses the efficient level of investment:

10Any σ > pmax

1−pmaxwould do.

14

Lemma 3 After peace, if the cost of capture is high (kc = k) or the value of externalities is

low (σ = σ), then C chooses the efficient level of investment, i.e. be such that S ′ (be) = kb1+σ

.

Proof. Straightforward.

Now consider the case where the cost of capture is low and the value of externalities is

high. C anticipates that it will not get the full value of the surplus it creates, because H will

capture the market. In order to create a strictly positive surplus, C must obtain terms that

are sufficiently generous, for otherwise it would prefer not to invest in butter and get a payoff

of zero. If the value of the externalities is sufficiently high, however, C would always prefer

to produce a strictly positive surplus and this constraint is non-binding. Mathematically,

C’s problem is to choose b to solve max− kbb + p(κ)S(b)(1 + σ)− cC . Since S is a concave

function, this problem is well defined and has a unique solution given by the following:

Lemma 4 After peace, if the cost of capture is low (kc = k) and the value of the externalities

is high (σ = σ), there is a value σ′′ such that for any σ > σ′′, C’s investment in butter is

b∗(κ) such that S ′ (b∗(κ)) = kbp(κ)(1+σ)

. Proof. Straightforward.

We notice that C’s investment in butter is too low, relative to the efficient level (for a

graphical illustration, see Figure 2). C anticipates that it will reap only part of the benefit

of its investment, because H cannot commit to refrain from capturing the surplus. In this

sense, peace is inefficient. By contrast, war would lead to the efficient level of investment,

because the victor V would reap the full benefit of its investment (contrast lemmas 1 and 4).

—Figure 2 about here.—

We now ask whether H and C could bargain peacefully over the control of the resources,

setting an appropriate transfer T such that C would be allowed to exploit the resources.

Write Uw,i for the payoff after peace (w = P ) or war (w = W ), for country i (i ∈ {C,H} in

peace and i ∈ {V, L} after war). The maximum transfer T that C is willing to make to H15

is such that −T + UP,C ≥ p(κ)UW,V + (1 − p(κ))UW,L − cC . The minimum transfer T that

H requests from C is such that T + UP,H ≥ (1− p(κ))UW,V + p(κ)UW,L − cH . A bargaining

range exists, and thus peace prevails, if and only if

(UW,V + UW,L)− (UP,H + UP,C) ≤ cC + cH (1)

The right-hand side of the inequality is strictly positive, since war is costly. Given the

above, the left-hand side of the inequality is weakly positive. A victor chooses the efficient

level of investment after war, since it expects to reap the full benefit of its investment. In

contrast, a challenger may choose a sub-optimal level of investment. Since the hegemon

cannot commit to refrain from using its influence on the international market, the challenger

may expect to reap only part of the benefit of its investment in a surplus of butter and thus

choose an inefficiently low level of investment. Peace prevails if and only if this inefficiency

is smaller than the cost of war.

Note that this condition for war results from a commitment problem that is different from

the standard commitment problem in the literature (see, e.g. Powell (2006, 182)). In the

standard argument, a rising state cannot commit to refrain from using its future military

power. When the shift in the distribution of power is greater than the cost of war, conflict

ensues. In such a situation, the declining power prefers war even if it were to receive the

full value of the pie in the current period. In our model, the hegemon cannot commit to

refrain from using its economic influence over the international market. War ensues when

this commitment problem leads the challenger to make an investment that is too low, creating

an inefficiency that eliminates the bargaining range created by the cost of war. As such, the

standard argument for war is one where war occurs because of a feasibility constraint: the

minimum demand of one state is less than the maximum offer of the other state, but the

bargaining range does not intersect with the set of feasible offers. In contrast, our argument

is that war results from a compatibility constraint: the minimum demand of one state is

greater than the maximum offer of the other state.

16

Let us characterize the conditions under which war happens in our setting. Assume that

the cost of capture is high or the value of the externalities is low. Because C is confident

that H will not capture any part of the surplus that it creates, C chooses the efficient level

of investment (lemma 3). Therefore, whether or not peace prevails, players expect the same

surplus to be created and thus peace prevails, given that war is costly. The left-hand side of

condition (1) is zero, which is strictly less than the right-hand side.

Now assume that the cost of capture is low and the value of the externalities is high.

In these circumstances, H would capture the market if a surplus is created. Capturing the

market is costly in and of itself, and the expectation of such a capture leads C to invest at

a sub-optimal level, making peace inefficient. The left-hand side of condition (1) is strictly

positive and the condition may fail, in which case war would ensue.

Therefore, any factor increasing the expected cost of capture is a force for peace. The

strength of international institutions and the size of the challenger’s sphere of influence, by

increasing the probability that the cost of capture is high, thus reduce the probability of war.

In addition, when the cost of capture is low and the value of the externality is high, the

inefficiency of peace decreases with C’s capabilities, κ. Indeed, total payoffs after war are

fixed. Total payoffs after peace increase continuously with κ. The greater is κ, the greater is

the share of the surplus that the challenger expects to obtain, and the closer is its investment

to the efficient level. Summing up the above discussion:

Proposition 1 (i) War occurs if and only if the cost of capture is low, the value of the exter-

nalities is high, and the exogenous capabilities of the challenger are low; (ii) The probability

of war is decreasing with the size of the challenger’s sphere of influence and with the strength

of international institutions. Proof. See the Appendix.

4.3 Robustness and Extensions

We build on the results of the previous sections to discuss the relationship between power

and war. A standard argument in the literature relates power shifts to the incidence of war.17

A state could rationally go to war so as to prevent exogenous shifts in the balance of power

if they are large and rapid (Fearon, 1995; Powell, 2006). A rising state, by contrast, should

not go to war, as it benefits from the continuation of peace.

The first difficulty with this argument is that such exogenous, large and rapid shifts in

the balance of power are rare (Debs and Monteiro, 2014). The second difficulty is that

any evidence of a rising state deciding to go to war appears to contradict the rationalist

framework. By at least some metrics, Japan and Germany were rising before the start of

the Second World War. Perhaps they feared a decline, but how do we assess counterfactual

trends in power? Given the prominence of these examples, we discuss them in greater detail

below.

Part of the appeal of the rationalist argument is that it appears sensible that if a state

is to go to war, it should do so under the best possible terms. A declining state should go

to war before it declines in power. A rising state should wait before going to war. Yet it is

one thing to explain the timing of war and another to explain the cause of war. A theory

of war is not complete if it explains the breakout of war by assuming that war would have

happened in the future if peace were to prevail in the present.

Our framework addresses these issues by insisting on the importance of power levels

instead of power shifts as a cause of war. A hegemon cannot commit to refrain from using

its influence on the international political economy. When a challenger is too weak to obtain

favorable terms of peace, it expects its growth to be stunted, making war a rational option.

A natural extension of our argument is that a rising challenger may declare war before

its rise in power. Consider a two-period game in which the challenger’s power rises between

periods 1 and 2, whether or not peace prevails. Quite simply, if the challenger is too weak

in period 2 so that war would obtain then, then a fortiori the challenger is also too weak

in period 1, so that war happens before the challenger’s power rises.11 This does not mean

that the shift in power is the cause of the conflict.12 Instead, our argument highlights the

11See lemma 5 in the Appendix.12War obtains even if it does not affect the power trajectory of the challenger.

18

importance of power levels on the initiation of conflict.

In this vein, we consider two extensions of our baseline model, endogenizing the balance of

power. A first natural extension is to let the challenger increase its capabilities by investing

in ‘guns.’ Perhaps war could be avoided if C could increase its capabilities through this

investment. This is not the case.13 H’s commitment problem induces C to over-invest in

guns as well as under-invest in butter. As a result, H’s commitment problem may still lead

to war. Moreover, note that, as in the main model, the lower are C’s exogenous capabilities,

the greater is the inefficiency of peace, and the more likely war becomes.14

In a second extension, we expand the baseline model to an infinite horizon. Perhaps with

an infinite horizon, H could be disciplined not to capture the surplus generated by C by

appropriate punishments off the equilibrium path.

To investigate whether this is the case, we allow for two dynamic effects on the challenger’s

capabilities. First, we introduce the possibility that the current division of the surplus affects

the future balance of power. Second, we vary the consequences of war on future military

capabilities. A standard assumption in the literature is that war is a ‘game-ending move,’

where the victor V would win all future wars. Yet the intuition behind the argument that the

threat of future punishment could enforce cooperation is captured most easily if war is not

a game-ending move. Here we introduce a flexible set-up where the breakdown of peace in

period t ensures the victor V to win any war for the next N periods. After these N periods,

the challenger’s capabilities return to their pre-war level. We call N the effectiveness of war

and we say that during these N periods the loser L does not have military capabilities.

First we note that peace is not easy to sustain in an infinite-horizon game when the

pie to be divided by the states is endogenous. Indeed, we show that there is a Markov

Perfect Equilibrium (MPE) where war occurs in every period, when both states have military

capabilities, under some conditions.15 Anticipating that there would be a future war, H

13See lemma 6 in the Appendix.14See proposition 2 in the Appendix.15See lemma 7 in the Appendix. In a Markov Perfect Equilibrium, strategies are Markovian in that they

19

captures any surplus created by C, and anticipating that its surplus would be captured, C

under-invests in butter. Peace becomes inefficient and war breaks out in the current period.

This result stands in contrast with standard models, where peace prevails when the pie is

exogenous and constant over time (Fearon, 1996; Powell, 2013).

Second we show that the threat of future punishment is insufficient to avoid war when the

division of the surplus affects the challenger’s future capabilities.16 When there are dynamic

consequences to peace, war may happen because H is tempted to capture the surplus so as

to prevent C from becoming more powerful. Anticipating this, C under-invests in butter,

making peace inefficient. In fact, as the effectiveness of war increases to infinity, conflict

occurs for any parameter configuration. The cost of war creates a bargaining range around

the players’ relative capabilities in each period, but this range is arbitrarily small as the

effectiveness of war goes to infinity – the cost of war is paid once but the benefit of disabling

the enemy is enjoyed for an infinite number of periods. If the division of the pie affects future

power, then, the bargaining ranges before and after the division of the surplus do not overlap,

making conflict unavoidable.

Put differently, war may occur when there are externalities in the division of the surplus.

This was captured in reduced form in the variable σ in the baseline model, and can be

captured by the dynamic consequences of the division of the surplus in an infinite-horizon

game, holding fixed σ.

5 Empirical Illustrations

We now apply our framework to shed new light on the causes of the Second World War in

Europe and the Pacific. In both cases, economic motivations were of central importance.

Germany and Japan depended on the United States for access to vital resources they needed

depend on history only through the payoff-relevant state variable, in this case C’s capabilities, and they forman equilibrium if they are mutual best responses.

16Such a threat could sustain peace, however, if the division of the surplus does not affect the challenger’sfuture capabilities. See lemmas 8 and 9 in the Appendix.

20

for economic growth – capital and oil, respectively. Neither country controlled spheres of

influence that ensured unrestrained access to the resources it needed for growth. Furthermore,

international economic interactions at the time were weakly institutionalized.

When the strategic value of the resources Germany and Japen needed for growth increased

for the United States, Washington restrained their access to them. This change produced

serious hold-up problems in their economies, contributing to Berlin’s and Tokyo’s decisions to

go to war despite their relative weakness. Relative to the United States, the largest economy

in the world at the time, Germany grew from 31% in 1929 to 43% in 1938, the year before

war broke out. The Japanese economy, for its part, went from 15% of the U.S. economy in

1929 to 23% in 1940, the year before Japan attacked the United States.17 As such, WWII

constitutes an important historical case of war launched by middle powers, at least partially

for the economic hold-up reasons captured by our mechanism.

5.1 The Economic Causes of World War II in Europe

Explanations for WWII in Europe focus on the Western Powers’ decision to shift from a

strategy of appeasing Germany to a strategy of confronting it (Powell, 2006; Taliaferro,

Ripsman and Lobell, 2013). After successive concessions, France and the United Kingdom

concluded that Hitler could not be appeased and declared war on Germany in response to

Berlin’s invasion of Poland on September 1, 1939. Had the Western Powers decided to stop

German gains even earlier, the argument goes, war would have happened sooner (Ripsman

and Levy, 2007).

This explanation is incomplete, however, accounting only for the timing of the war. The

causes of the war are assumed: Hitler had an insatiable revisionist strategy, so peace could

not have prevailed. That Hitler’s strategy was morally repugnant does not mean it was

entirely irrational. To capture the causes of the war, we need to account for the origins of

Germany’s expansionistic policy aims.

17Source: Bolt and van Zanden (2014); values in constant 1990 international dollars.

21

The basic strategic dilemma faced by Germany since the end of World War I was straight-

forward. It could try to grow peacefully or attempt another militarized challenge to the

international order. Given Germany’s limited markets for inputs and outputs, and its debt

to the victors of World War I, a peaceful growth strategy depended on a permissive interna-

tional environment. Such a situation prevailed until the early 1930s. During that time, the

peaceful growth strategy, put forth most notably by Gustav Stresemann (Berlin’s Foreign

Minister between 1923 and 1929), dominated German politics.

After the 1929 crash, however, capital became more valuable for the United States and

credit markets tightened. Washington repeatedly refused German requests for loans, a mani-

fest “failure in leadership” (Kindleberger, 1986, 133; see also: Leffler, 1979, 194-195, 228-229;

Clavin, 1996, 16). In Germany, the peaceful-growth strategy was discredited. Hitler’s views,

which called for the overthrow of Versailles if necessary by force in order to guarantee Ger-

many’s growth, went from a fringe position by 1928 to a widely held creed in Germany by

1933.

In our view, the profound change in Germany’s ability to access capital – a resource vital

for its economic growth – at the turn of the 1930s played a crucial role in boosting the case

of those in Germany, Hitler among them, who argued that a military confrontation was the

best path towards German growth. Germany’s inability to access capital after the onset of

the Great Depression in the United States was an important economic factor contributing to

the onset of WWII in Europe.

The 1919 Versailles Treaty required Germany to pay substantial reparations to Allied

powers for causing WWI (Trachtenberg, 1980; Schuker, 1988; Kent, 1989; Boemeke, Feldman

and Glaser, 1998; Cohrs, 2006). After initial resistance, Berlin agreed to payments starting

in 1921, and pursued a strategy of seeking eventual revision of its obligations through the

fulfillment of its payment requirements (Trachtenberg, 1980; Webb, 1989; Ferguson, 1996).

Soon thereafter, however, Germany defaulted on reparation payments, triggering a chain of

events that led the German currency to collapse, producing hyperinflation (Schuker, 1988;

22

Ferguson, 1996). Furthermore, this crisis prompted Washington to attempt to create a more

stable “reparations regime” in order to ensure European stability (Costigliola, 1984, 119-123;

Cohrs, 2006, 137). The resulting Dawes Plan of 1924 lowered German reparation payments

for 1924-27 and included a large U.S. private loan to the German government, leading to a

boom in U.S. private loans to Germany (Marks, 1978, 245-249; Schuker, 1988). In effect,

U.S. lending to Germany created a financial “merry-go-round” in which all participants had

a stake: Germany obtained credit from the United States, enabling it to make reparation

payments to Britain and France, which could then repay their inter-allied war debts to the

United States (Tooze, 2006, 6).

For Berlin, this meant financial dependency on Washington, and by 1927 “German de-

pendence on American capital seemed to be an inevitable fact of life” (McNeil, 1986, 161).

Yet the economic benefits were substantial. The flow of American capital into Weimar Ger-

many was “one of the greatest proportional transfers of wealth in modern history” (Schuker,

1988, 120). Germany received far more funds in U.S. private loans (27 billion marks) than

the totality of the reparations it had to pay (19.1 billion marks) in 1921-1931 (Marks, 1978,

254). The rise in standards of living made possible by the inflow of American credit also had

a clear political effect. In the May 1928 federal election for the German Reichstag the Nazis

achieved no more than 2.5 percent of the votes even in their stronghold, Bavaria (Tooze,

2006, 12-13). As late as 1928, then, the Weimar Republic continued working as a political

system focused on achieving economic growth through cooperation with the United States.

This favorable international environment soon came to an end. Starting in late 1928,

the U.S. credit market tightened and interest rates rose, ending long-term loans to Germany

(McNeil, 1986, 217-219; Tooze, 2006, 14). Unable to access U.S. capital in favorable terms,

Germany demanded another revision of the reparations regime, resulting in the Young Plan

of June 1929, which, among other things, consolidated German dependency on U.S. capital,

by relying on loans by U.S. banks to finance the majority of the payments (Leffler, 1979, 195,

202-216, 228-229; Enssle, 1980, 182; Costigliola, 1984, 210-217). But even before the Plan

23

would come into effect in January 1930, the U.S. economy suffered the October 24, 1929,

“Black Thursday” stock market crash (Leffler, 1979, 215-216; Kindleberger, 1986, 118). The

near-collapse of the U.S. financial system meant that German access to private U.S. capital

was now much reduced. As Carl von Schubert, the state secretary at the German foreign

ministry said at the time, “A direct demand on the foreign market by the Reich government

for either long- or short-term loans is no longer a possibility” (quoted in McNeil, 1986, 269).

In Germany, therefore, the onset of the U.S. Great Depression discredited the peaceful-

growth strategy. Over the next three years, U.S. banks drastically curtailed the availability of

capital to the German economy.18 As Burke writes, “it was American policy that established

the system of international exchange. The cycle of reparations and war debts payments was

financially dependent on American loans. When the outflow of capital from the United States

dried up, the system was bound to founder” (Burke, 1994, 128).

Consequently, Germany experienced a sharp drop in national income and industrial pro-

duction, with unemployment rising dramatically (Kolb, 2004, 111). By the time Hitler was

appointed Chancellor in early 1933, a third of the labor force was unemployed (Kolb, 2004,

111). The Nazis actively portrayed this situation “as a consequence of the ‘system,’ and

ruthlessly mobilized open and latent resentment of parliamentary democracy” (Kolb, 2004,

112). In sum, the onset of the Great Depression produced “political and economic circum-

stances combined with the public mood to create a situation especially favorable to National

Socialist agitation and action” (Kolb, 2004, 108). Over the following three years, the Nazis

went from an obscure fringe political group to become Germany’s main political party.

Already in the September 1930 election, the Nazis became the second largest party in

parliament. When in May 11, 1931, an Austrian banking crisis broke out, “the withdrawal of

German short-term credit became a flood” (Clavin, 1996, 12). The credit shortage triggered

a German financial crisis (Costigliola, 1984, 235), prompting Chancellor Bruening on June

18Many claim that the German economic trouble was compounded by the protectionist Smoot-HawleyTariff Act trade of June 1930 (Costigliola, 1984, 231; Tooze, 2006, 14). As Irwin (2012, 15-16) shows, thismeasure had a limited impact.

24

6 to issue “an aggressive demand for an end to reparations” (Tooze, 2006, 18). The quickly

deepening crisis led to the June 20, 1931, Hoover moratorium, which froze German reparation

payments (Marks, 1978, 253; Clavin, 1996, 14), but failed to stem the flight of foreign capital.

Despite the moratorium, “[m]oney continued to flood out of Germany at a faster rate than

before” (Clavin, 1996, 16). Weeks later, a German banking crisis broke out, prompting a

general bank run (Costigliola, 1984, 238) and leading the Berlin cabinet to close down the

entire German financial system, abandon the free gold standard, and nationalize all private

holdings of foreign currency (Tooze, 2006, 20).

In an attempt to stop the damage, an international financial conference was held in Lon-

don in July 1931, including the United States. Delegates agreed “that the central bank credit

of $100 million [to the Reichsbank] should be renewed, [that] a standstill of existing credits

should be implemented, and [that] a committee to study Germany’s long-term needs should

be established” (Leffler, 1979, 255). This meant further U.S. involvement in European affairs

(Leffler, 1979, 256). The Standstill agreement was put in place in August-September 1931

and “Weimar’s foreign creditors voluntarily agreed to freeze their credits inside Germany”

(Clavin, 1996, 16).

Having left the gold standard, the German currency could quickly lose value. As German

debts were mostly denominated in foreign currency, any devaluation would have the effect of

putting at stake Germany’s ability to service its foreign debt. Washington therefore leaned on

the Berlin government to impose exchange controls (Irwin, 2012). Berlin complied in a last-

ditch attempt to cling to its Atlanticist, peaceful-growth strategy: “Chancellor Bruening’s

government gambled that, sooner rather than later, American action on war debts would

enable Britain and France to accept the end of reparations. This ... would open the door

to the normalization of both political and economic relations in Europe” (Tooze, 2006, 22).

Alas, any discussion of the end to reparation payments and inter-Allied war debts would

have to wait for another year, until the July, 1932, Lausanne Conference. In the meantime,

the German economy continued its downward spiral – dragging with it the peaceful-growth

25

strategy that defined Weimar foreign policy.

By late 1931, as Bruening continued to impose deflationary austerity measures by decree

amid a widespread financial and economic crisis, his government’s political support collapsed.

The deep transformation of the international economy over the previous two years had played

a prominent role in the ongoing political shift in Germany: “Nationalist visions, visions of a

future in which global financial connections were not the determining influence in a nation’s

fate, now had a far greater plausibility” (Tooze, 2006, 23-24).

The Hoover administration made its last attempt to solve the crisis at the Lausanne

Conference, which discussed German reparation payments and inter-Allied war debts (Clavin,

1996, 31). Representatives of Britain, France, and Germany recognized Germany’s inability

to restart reparation payments and agreed to prolong their suspension and, more importantly,

cancel about 90% of German reparations (Costigliola, 1984, 257; Marks, 1978, 253-254). This

agreement had a glitch, however. It depended on U.S. pardon of most British war debts

(Cohrs, 2006, 44), which would be rejected by the U.S. Congress in December 1932.

By then it was too late to save the Weimar Republic. In the March 1932 German pres-

idential elections, President Hindenburg had been reelected but required a runoff to defeat

Hitler by 54%-37% (Burke, 1994, 190-192). Then, in the parliamentary election of November

that year, the Nazis retained 196 seats, consolidating their position as the first political force

in Germany. On January 30, 1933, Hindenburg appointed Hitler as Chancellor. Hitler’s

government would repudiate both reparations and war debts, making no further payments.

Instead, Hitler led Germany in a crash militarization program aimed at challenging the U.S.-

led global order.

The importance of the United States in Hitler’s thinking tends to be overlooked. It is

best articulated in his Zweites Buch, in which Hitler’s well-rehearsed arguments on the need

to rearm the nation, followed by a military conflict aimed at acquiring sufficient Lebensraum

for the German people – a goal that required the destruction of the Soviet Union and the

annihilation of its population – are presented as merely a means to an end: a struggle for26

world domination between a German-controlled Europe and the United States. In historian

Richard Evans’ words, the core of Hitler’s foreign policy was to “create in eastern Europe

what he thought of as the equivalent of the American West – a kind of bread basket for

Germany. Somewhere where industrial resources, agricultural resources, would make Ger-

many into a world power capable of standing head-to-head with America in the longer run”

(Evans, n.d.).19 In Hitler’s strategic vision, “Fordist” America – his preferred term for the

industrialized economy of the United States – was both Germany’s ultimate competitor and

its greatest role model. Germany needed an equally vast domestic market. Without the scale

of America’s natural and human resources, Hitler thought, Germany would be destined to

have the status of “Holland or Switzerland or Denmark” (Hitler, 2003, 128). As Tooze (2006,

10) put it, “Fordism ... required Lebensraum,” concluding:

America should provide the pivot for our understanding of the Third Reich.

In seeking to explain the urgency of Hitler’s aggression, historians have underes-

timated his acute awareness of the threat posed to Germany ... by the emergence

of the United States as the dominant global superpower. ... The originality of

National Socialism was that, rather than meekly accepting a place for Germany

within the global economic order dominated by the affluent English-speaking

countries, Hitler sought to mobilize the pent-up frustrations of his population

to mount an epic challenge to this order. ... Germany would carve out its own

imperial hinterland; by one last great land grab in the East it would create a self-

sufficient basis both for domestic affluence and the platform necessary to prevail

in the coming super-power competition with the United States. (Tooze, 2006,

xxiv)20

19Specifically, Hitler projected a final military showdown with the United States. As he wrote, “it isthoughtless to believe that the conflict between Europe and America would always be of a peaceful economicnature” (Hitler, 2003, 116). America’s role in Hitler’s strategic vision helps account for what is perhaps themost catastrophic strategic decision of the twentieth century: Hitler’s declaration of war on the United Statesin December 1941, which was not required by Berlin’s treaty obligations towards Tokyo.

20See also Tooze (2006, 656-671). Tooze (2006) documents, convincingly, the difficulty of such a militarychallenge to the U.S.-led order, showing how once the German blitzkrieg strategy failed against the SovietUnion in 1941, Germany was fated to lose the war, given the relatively small size of its economic base.

27

To summarize, as an economic hegemon with a large influence on financial markets, the

United States had for most of the 1920s bankrolled the recovery of the German economy.

When capital became scarce in the aftermath of the 1929 U.S. stockmarket crash, however,

Washington failed to take the steps necessary to ensure continued German access to capital

markets, creating a serious hold-up problem in the German economy. Unable to grow in the

international economic structure that resulted from the Great Depression, Germany shifted

to a policy of military challenge to the status quo. This policy, as demonstrated by a careful

reading of Hitler’s worldview, ultimately aimed at defeating the United States and imposing

on Washington more beneficial terms of international interaction.

5.2 The Economic Causes of World War II in the Pacific

There is a vast debate on the causes of WWII in the Pacific. Some scholars question the

usefulness of a rationalist approach to the conflict, claiming that it was due to excessive

optimism on the part of the Japanese (Snyder (1991, chapter 4); Taliaferro (2004, chapter

4); Record (2009, 1-5)). Others accept a rationalist account, arguing that, when compared

to the decline to which peace fated Japan, war was the lesser of two evils (Russett, 1967).21

Yet no account explains the strategic underpinnings that led Japan to conclude that war was

the lesser evil.

Our framework sheds light on how the economic interaction between the United States and

Japan was at least in part responsible for WWII in the Pacific. Economic motivations were

a key driver of Japanese foreign policy in the lead-up to the war. With limited resources

of its own, Japan was highly dependent on foreign markets for raw materials, including

energy. In a series of endeavors since the late 19th century, Japan gradually acquired access

to additional economic resources by conquering territory in East Asia: Taiwan after the first

21Another set of scholars claim that the war was due to bureaucratic overreach in Tokyo (see: Russett(1967, 99); Sagan (1988, 916)) or in Washington (see: Utley (2005); Sagan (1988)). Finally, there is a debateon whether FDR adopted a tough policy to deter an attack on the USSR (Heinrichs, 1988, 1990) or provokethe Japanese as a back-door entry into a war with Nazi Germany (see Trachtenberg (2006); Schuessler (2010);Copeland (2014) and the debate in Reiter and Schuessler (2010)). We discuss these views below in footnote22.

28

Sino-Japanese War (1894-5); the Liaotung peninsula, after the Russo-Japanese war (1904-5);

and resource-rich Manchuria, in March 1932 (Barnhart, 1987, 27-33). Continuing Japan’s

drive to control additional resources, the long and costly second Sino-Japanese war erupted

in 1937. Three years later, in August 1940, Japanese foreign minister Matsuoka Yosuke

expanded the projected sphere of influence, now called the “Greater East Asia Co-Prosperity

Sphere,” to include Australia, Borneo, Burma, India, Indochina, Malaya, New Zealand, the

Dutch East Indies, and Thailand (Iriye, 1987, 131; LaFeber, 1997, 192-193).

The United States consistently opposed these Japanese attempts to establish a sphere of

influence in Asia. Washington had a long-standing commitment to defend the Open Door

policy in China. In fact, according to historian Walter LaFeber, “[e]verything [U.S. Secretary

of State Cordell] Hull had tried to achieve since he had entered the State Department was

aimed precisely at destroying such regional blocs and Japan’s (or any non-American) ‘Monroe

Doctrine.’ Roosevelt, with less passion, agreed” (LaFeber, 1997, 193). After the escalation

of hostilities in the second Sino-Japanese war in 1937, Roosevelt made a famous “Quarantine

Speech,” calling for “peace-loving nations” to contain the spread of war (Barnhart, 1987, 123;

Utley, 2005, 16). Furthermore, the United States imposed a series of “moral embargoes” on

Japanese trade.

Germany’s invasion of the Soviet Union in June 1941 presented Japan with a window of

opportunity to grab the territories it needed to control the resources necessary for economic

expansion (see, e.g., Heinrichs (1990); LaFeber (1997, 197)). Foreign Minister Matsuoka

favored an immediate attack on the Soviet Union (Ike, 1967, 60). Well aware of this strategic

situation, Washington worried that Tokyo would open a second front against the USSR,

which was already overwhelmed by the German Operation Barbarossa (see, e.g. Wohlstetter

(1962, 107,126)). Such a development would endanger the survival of the Soviet Union,

making it possible for the entire Eurasian landmass to fall under the control of the Axis

powers.

At the Imperial Conference of July 2nd, the cabinet decided instead to proceed with

29

a Southern Advance – aimed at accessing resources in Southeast Asia, particularly oil –

“no matter what obstacles may be encountered” (Ike, 1967, 78). Japanese leaders became

increasingly convinced that war with the United States was inevitable. As Prime Minister

Konoye clarified: “In carrying out the plans outlined . . . we will not be deterred by the

possibility of being involved in a war with England and America,” noting that “all plans,

especially the use of armed forces, will be carried out in such a way as to place no serious

obstacles in the path of our basic military preparations for a war with England and America”

(quoted in Wohlstetter, 1962, 345-346).

On July 24th Japan launched the Southern Advance. The next day, the United States

responded with a complete embargo on sales of oil to Japan. Importing so much of its oil from

the United States, Japan faced two undesirable choices: war against a much stronger economy

or economic collapse (Wohlstetter, 1962, 356-357). The Japanese government eventually

reached the conclusion that its policies were “mutually incompatible” with those of the

United States, so that the conflict “will ultimately lead to war” between the two countries

(Ike, 1967, 152).

After months of tense negotiations, Japanese decision-makers chose war, and on December

7th, 1941, attacked the U.S. Pacific Fleet at Pearl Harbor. Whether or not the cabinet

debated the strategic consequences of a direct attack, it had endorsed a war with the United

States. In retrospect, the failure to anticipate the effect of an attack on Pearl Harbor may

help explain why Japan opted for this risky opening gambit, which may in turn help account

for the outcome of the conflict. But it does not explain the initiation of war itself.

In sum, international conditions made Tokyo’s decision to go to war compelling. Japan’s

inability to access the necessary resources for economic grow in the world economic system

dominated by the United States contributed to Tokyo’s decision to launch a war. Japan

was relatively weak and dependent on access to foreign resources that were to a great extent

controlled by the United States. When the strategic value of a key resource – oil – increased,

the United States restricted Japanese access to it, and Japan initiated the Pacific War.

30

By declaring war on the United States, Japan took on a much stronger enemy, which had

far more latent power and ultimately imposed severe damage and obtained unconditional

surrender. Our mechanism highlights how the serious economic hold-up problem faced by

the Japanese economy in the summer of 1941 led decisionmakers in Tokyo to prefer such a

conflict to the maintenance of peace with the United States. War could be attractive even

if it was costly, because victory would allow Japan better to solve its hold-up problem and

convert its economic resources into output efficiently.22

6 Conclusion

This article introduced a theory of the economic roots of war, explaining how the need

to access the resources necessary for efficient economic growth may produce incentives for

conflict. We illustrate this mechanism for war to the run-up of WWII in Europe and the

Pacific. Germany and Japan lacked access to key resources, capital and oil respectively,

which underpinned their decision to military challenge to the status quo.

More generally, our argument provides a framework for assessing the risks of war due

to economic motivations, shedding light on the historical pattern and providing lessons for

future scenarios. In comparison with U.S. interactions with Germany and Japan in the 1930s,

America’s rise in the late 19th century was more likely to remain peaceful. Since the United

States already possessed a sphere of economic influence on the American continent, bolstered

by the Monroe Doctrine, it was less likely that Britain would restrain U.S. access to resources;

which in turn made it less likely that Washington would challenge Britain militarily.

22A rationalist account focusing on the strategic calculations of war and peace is thus sufficient to explainthe war. It is unnecessary to refer to bureaucratic overreach in Japan; Japanese decision-makers clearlyendorsed a decision to declare war on the United States. It is unclear that there was bureaucratic overreachin Washington. Indeed, the argument that FDR lost control of policy is disputed (see: Heinrichs (1988, 141-142); Heinrichs (1990, 165); Schuessler (2010, 159); Trachtenberg (2006, 99-100)). It appears that Achesonwas instructed by under-Secretary Sumner Welles to deny requests for oil while Roosevelt was meeting withChurchill (Heinrichs, 1990, 165). There is good reason to believe that Welles was conveying Roosevelt’spreferences. Roosevelt knew that the oil embargo may drive Japan to aggressive action, and he certainlyconsidered the possibility of relaxing the embargo if necessary (see, e.g., Trachtenberg, 2006, 96, 98). A toughpolicy towards Japan would have made sense for FDR whether he wished to deter Japan from attacking theUSSR or induce them to attack the United States so as to take the country into war with Nazi Germany.

31

With the end of the Second World War, two factors have reduced the odds of great power

conflict. First, nuclear weapons have raised the cost of war. Second, the institutionalization

of trade has increased the cost of economic capture for the United States, the largest economy

on earth. Taken together, these dynamics highlighted by our model are compatible with the

relatively lower incidence of interstate conflict since 1945.

Applying these lessons to the U.S.-Soviet rivalry, we see that there was little economic

incentive for a direct confrontation. Both countries controlled significant markets for goods

and resources. Furthermore, the two blocs traded little between them, limiting Washington’s

ability to restrict Soviet access to the resources necessary for economic growth. For the Soviet

Union, fighting over additional markets would be highly unlikely to bring about faster growth,

particularly in light of the potential destruction brought about by nuclear war. Despite the

intense rivalry between the United States and the Soviet Union, competition between the

two superpowers never broke into direct military conflict.

Looking ahead, we can use this framework to analyze the odds that U.S.-China rela-

tions will remain peaceful. Given both countries’ nuclear status, the costs of war remain

particularly high. Furthermore, and although China possesses a large and growing domestic

market, Beijing is relatively dependent on access to international markets for its economic

growth. This could present a problem for peace. At the same time, Washington would pay

a high cost to attempt to restrict Chinese access to these markets, due to the high degree of

institutionalization of the international economy, namely, the fact that China is a member

of the World Trade Organization. As a result of these high costs of war and market capture,

the economic dimension of U.S.-China relations is a force for peace.

7 Online Appendix

This Appendix consists of three parts. Section 7.1 presents a proof of the formal results

of the baseline model (section 4.2). Section 7.2 presents a formal description of the results

in the extensions of the baseline model (section 4.3). Section 7.3 presents a proof of these32

results.

7.1 Baseline Model: Proof of the Results

The proofs of lemmas 1 to 4 are straightforward and therefore omitted. Here we present the

proof of proposition 1.

Proof. (Proof of proposition 1). Given lemmas 1 to 4, we conclude that the following

form equilibrium strategies of H and C’s bargaining over T . H’s strategy is as follows: if

condition (1) holds, then H demands T = TC ; if condition (1) fails, then either H declares

war or demands T > TC .23 C’s strategy is to accept T if and only if T ≤ TC , where

TC = UP,C − p(κ)UW,V − (1− p(κ))UW,L + cC (2)

and payoffs Uw,i are as described below.

Consider Part (i). Payoffs after war are UW,L = 0 and UW,V = −kbbe + S(be)(1 + σ) so

that total payoffs after war are

UW,V + UW,L = −kbbe + S(be)(1 + σ) (3)

Payoffs after peace depend on the cost of capture and the value of externalities.

First consider the case where the cost of capture is high or the value of externalities is

low, (kc, σ) 6= (k, σ). Then UP,H = 0 and UP,C = UW,V . Therefore, UP,H+UP,C = UW,V +UW,L

and condition (1) holds.

Now consider the case where the cost of capture is low and the value of externalities is

high, i.e. (kc, σ) = (k, σ). We have UP,C = −kbb∗(κ) + p(κ)S(b∗(κ))(1 + σ)− cC and

UP,H = −k + (1− p(κ))S(b∗(κ))(1 + σ) + cC ,24 so that total payoffs after peace are:

23Though it might be more reasonable to have H demand T ≥ −UP,H + (1− p(κ))UW,V + p(κ)UW,L− cH ,any demand T > TC is rejected and can be offered in equilibrium.

24We exploit the fact here that σ is sufficiently large.

33

UP,C + UP,H = −k − kbb∗(κ) + S(b∗(κ))(1 + σ) (4)

First note that the difference in total payoffs, after war and peace, is strictly positive ∀κ,

i.e. (UW,V + UW,L)− (UP,C + UP,H) > 0 since k > 0 and b∗(κ) < be.

Second note that the difference in total payoffs, after war and peace, is decreasing in κ.

Indeed, total payoffs after war are independent of κ. Total payoffs after peace are increasing

in κ since b∗(κ) is increasing in κ and b∗(κ) < be.

This completes the proof of part (i).

Consider Part (ii). Note that the ex ante probability of war is zero if the inefficiency of

peace is smaller than the cost of war, and ρk(η, θ)(1−ρσ) if the inefficiency of peace is greater

than the cost of war. Since ρk(η, θ) is decreasing in η and θ, then the ex ante probability of

war is decreasing in η and θ.

7.2 Robustness and Extensions: Description and Results

7.2.1 Exogenous Power Shifts and War

We now investigate the possibility that the challenger’s capabilities are rising exogenously

over time. Consider a simple two-period game where, in each period, the game follows the

timing of the baseline model and the challenger’s capabilities in period t are κt. In particular,

period 2 proceeds as in the baseline model, with the realization of the externalities and the

cost of capture and the negotiations over the transfer T between H and C, whether or not

peace prevails. We want to investigate the conditions under which a rising challenger would

wait to go to war. Put differently, if war is likely to happen in period 2, when does the

challenger refrain from going to war in period 1? As in the baseline model, we assume that

the value of externalities σ is sufficiently large. We can show:

Lemma 5 In a two-period game with exogenous power shifts and a rising challenger (κ2 >

κ1), if war would occur in period 2 when the cost of capture is low and the value of exter-34

nalities is high, then war occurs in period 1 when the cost of capture is low and the value of

externalities is high.

Proof. See section 7.3.1.

Put differently, the weaker C is, the less effective it is in using the threat of war to obtain

favorable terms of peace if H captures the market. If C is so weak in period 2 that war would

happen at that point, then war would also break out in period 1, when C is even weaker.

Note that war occurs because there is no bargaining range. Therefore, war could be declared

by either C or H. However, if H declares war, it would not be in order to prevent an adverse

shift in the balance of power; by assumption C is rising in power between periods 1 and 2,

whether or not peace prevails in period 1.

7.2.2 The Choice Between Guns and Butter

Now let us modify the baseline one-period model to allow C to invest in guns to improve the

balance of power in its favor. The timing is the same as in the baseline model, where the

player making the investment decision chooses a level of guns g at same time as it chooses

the level of butter b.

An investment in guns costs kg > 0 per unit and produces a favorable change in rela-

tive power. Let C’s total capabilities be the sum of its exogenous capabilities, κ, and its

investment in guns g, so that the probability that C wins a war after an investment in guns

is p(κ + g). (The probability that C wins a war before the investment in guns, i.e. when

bargaining over the transfer T , is p(κ)). As before, assume that the probability that C wins

the war is strictly between 0 and 1 and increases with greater capabilities at a decreasing

rate. Mathematically, this means that p(.) ∈ [pmin, pmax] ⊂ (0, 1), p′(.) > 0, p′′(.) < 0, and

limκ→∞p′(κ) = 0. We write the bounds on the possible values of exogenous capabilities κ as

κmin and κmax and assume that κmax is arbitrarily large.

As a benchmark, write ge and be for the efficient investment in guns and butter, respec-

tively, if it maximizes the total surplus, i.e. the vector that solves max−kgg−kbb+S(b)(1+σ).35

Efficiency requires an investment in guns equal to zero, i.e. ge = 0. Guns only serve to shift

the balance of power in favor of C without increasing the value of the surplus. Efficiency

requires a strictly positive level of investment in butter, be > 0, which remains the same as

in the baseline model, i.e. be is such that S ′(be) = kb1+σ

.

We solve the game by backward induction. After war, V chooses the efficient investment.

After peace, H captures the surplus if and only if the cost of capture is low and the value

of externalities is high. Moving up, C chooses the efficient level of investment if the cost of

capture is high or the value of externalities is low.

Now consider C’s investment decision if the cost of capture is low and the value of external-

ities is high. C’s problem is to choose b and g to solve max−kbb−kgg+p(κ+g)S(b)(1+σ)−cC .

This problem is well defined and has a unique solution, under general conditions on p(.) and

S(.) ensuring that the objective function is globally concave.25 The solution of this problem

is illustrated graphically in Figure 3.

—Figure 3 about here.—

The figure represents an ‘isocost function’ (kbb + kgg = k0) and an ‘indifference curve’

(p(κ + g)S(b)(1 + σ) = u0). There is a value of exogenous capabilities κs dividing up the

parameter space. A weak C (for whom κ < κs) is at an ‘interior solution,’ investing a strictly

positive amount in guns and bringing its total capabilities to κs. A strong C (for whom

κ ≥ κs) is at a ‘corner solution’ and does not invest in guns. Any C chooses a strictly

positive investment in butter, which is optimal given its total capabilities. If kg is sufficiently

large, no C invests in guns (κs = κmin). Summing up, C’s optimal level of investment can

be stated as follows:

Lemma 6 After peace, if the cost of capture is low (kc = k) and the value of externalities is

high (σ = σ), there is a value σ′′ such that for any σ > σ′′, the following holds:

25These conditions are given in the proof of lemma 6 below.

36

there is a value κs ∈ [κmin, κmax) such that C makes the following investment decisions:

a)for κ ∈ [κmin, κs), C chooses an investment in guns g∗ = κs−κ and an investment in butter

b∗(κs) defined by S ′ (b∗(κs)) = kbp(κs)(1+σ)

; b)for κ ∈ [κs, κmax], C chooses an investment in

guns g∗ = 0 and an investment in butter b∗(κ), defined by S ′ (b∗(κ)) = kbp(κ)(1+σ)

. Moreover, for

any σ, there is a value kg(σ) such that κs = κmin if kg ≥ kg(σ) and κs > κmin if kg < kg(σ).

Proof. See section 7.3.2.

Moving up, let us focus on the case where the cost of guns is not too high (kg < kg(σ)).

If the cost of guns is too high, then no C chooses to invest in guns and the analysis is the

same as in the baseline model, where we assumed that capabilities were exogenous.

Consider the round of bargaining between C and H over the control of the resources

and transfer T . A bargaining range exists, and peace prevails, if and only if condition (1)

holds. As in the baseline model, peace prevails if the cost of capture is high or the value

of externalities is low. Under either circumstance, C makes the efficient investment decision

and war is avoided, given that it is costly.

Now assume that the cost of capture is low and the value of externalities is high. In

these circumstances, H would capture any positive surplus. Anticipating such a capture,

C’s investment in butter is sub-optimal. Therefore, as in the baseline model, any factor

increasing the expected cost of capture is a force for peace. The strength of international

institutions and the size of the challenger’s sphere of influence thus reduce the probability of

war.

In addition, note that the inefficiency of peace is decreasing in C’s exogenous capabilities

κ. A weak C (for whom κ ∈ [κmin, κs)) chooses an investment in guns that brings its total

capabilities to κs and an investment in butter commensurate with these total capabilities.

Therefore, the stronger C is, the smaller is the investment in guns, and the lower is the

inefficiency of peace. A strong C (for whom κ ∈ [κs, κmax]) does not invest in guns and

choose an investment in butter that is increasing in its exogenous capabilities. Therefore,

the stronger C is, the more credible its threat to use force is, the greater is the share of the37

surplus that it expects to keep for itself, and the closer is its investment in butter to the

efficient level. In short, we obtain a result that is very similar to proposition 1:

Proposition 2 (i) War occurs if and only if the cost of capture is low, the value of the

externalities is high, and C’s exogenous capabilities are low; (ii) The probability of war is

decreasing with the size of C’s sphere of influence and with the strength of international

institutions. Proof. See section 7.3.2.

7.2.3 The Infinite-Horizon Game

Consider a game where the baseline model is played over an infinite horizon. We allow for

some flexibility in the dynamic consequences of peace and war over future military capabili-

ties.

First, if peace prevails, we introduce the possibility that the current division of the surplus

affects the future balance of power. Let κt be C’s capabilities at time t. Assume that if peace

prevails in period t, then C’s capabilities in period t+1 are (weakly) increasing in the amount

of surplus that it obtains in period t. Formally, κt+1 = f(κt, st), where st is the amount of

surplus that C obtains at peace in period t, st = zt if H captures the market and offers zt

and st = S(bt)(1+σt) if H does not capture the market. f(κt, st) is (weakly) increasing in st,

with f(κt, 0) ≤ κt ≤ f(κt, S(bt)(1+σt)). We will say that there are no dynamic consequences

to peace if f(κt, st) = f(κt, s′t) ∀st 6= s′t. In addition, we will ignore for now the possibility

of exogenous changes to the challenger’s capabilities - we analyze this possibility in a simple

two-period game above. Therefore, if there are no dynamic consequences to peace, then

f(κt, st) = κt = κ ∀t, st.

Second, if war obtains, we vary the effect of a war on future military capabilities. Let

the breakdown of peace in period t ensures that the victor V wins any war for the next N

periods, N ∈ N0 ∪∞, where we write “N = ∞” if the victor V would win any future war.

During these N periods, as in the baseline model, V makes the invesment decision, reaps

38

the full value of the surplus in the free market, and can choose to capture the market.26

After these N periods, the game follows the same timing as in the baseline model, and C’s

capabilities return to the pre-war level, κt. We will call N the effectiveness of war and we

will say that during these N periods the loser L does not have military capabilities.

Both countries discount the future by factor δ ∈ (0, 1). For simplicity, let us assume that

in every period the cost of capture is low and the value of externalities is high.

First, we show that there is a Markov Perfect Equilibrium where war happens in every

period, unless of course state L does not have military capabilites, under some conditions.

As discussed in the body of the paper, the logic is as follows. Anticipating that there would

be a future war, H captures the surplus as long as the value of externalities is high (relative

to the cost of capture). Anticipating that the surplus would be captured, C under-invests in

butter. Peace becomes inefficient and war happens in the current period. Formally, we state:

Lemma 7 There are values σ′ and δ′ such that for any σ > σ′, δ ∈ (δ′, 1), there is a

Markov Perfect Equilibrium where war occurs in every period where both players have military

capabilities, if and only if, for every t,

(UW,V + UW,L)− (UP,C + UP,H) >1− δ

1− δN+1(cC + cH) (5)

where UW,V + UW,L and UP,C + UP,H are the aggregate payoffs in the stage game, if war

and peace prevails in bargaining over T , and take the same value as in the baseline model.27

Proof. See section 7.3.3.

The proof of the lemma shows that if there are no dynamic consequences to war (N = 0),

then we retrieve the same condition for war as in the baseline model. Also, if war ensures

the victor to win all future wars (N = ∞), then war obtains for all κt and for all f(κt, st),

26We could let V request a transfer T from L at the start of a (future) period. In this case, L would bewilling to pay up to cL to avoid a war. Such an assumption complicates the algebra without changing theresults. We do not explore it here.

27More precisely, UW,V + UW,L = −kbbe + S(be)(1 + σ), UP,C + UP,H = −k − kbb∗(κt) + S(b∗(κt))(1 + σ),where b∗(κt) is such that S′(b∗(κt)) = kb

p(κt)(1+σ).

39

as long as players are sufficiently patient. Relative to war in period t+ 1, the benefit of war

in period t is to obtain an additional period of efficient investment. The drawback is that

the cost of war is paid in period t instead of period t + 1. As δ goes to 1, this drawback is

negligible. Therefore, for any value of κt, the inefficiency of peace is sufficiently high and war

obtains.

Next we ask the following question: if there is an MPE where war obtains in every period,

could efficient peace be sustained in a subgame-perfect equilibrium, if players are sufficiently

patient and any deviation triggers a reversion to the MPE where war obtains in every period,

when both states have military capabilities?

First we show that if there is no dynamic consequence to peace (and no exogenous change

in capabilities), i.e. f(κt, st) = κt = κ ∀t, st, then we can construct a stationary subgame-

perfect Nash equilibrium where peace prevails:28

Lemma 8 In the infinite-horizon game where there is no dynamic consequence to peace and

no exogenous change in capabilities (i.e. f(κt, st) = κt = κ ∀t, st), the efficient outcome can

be sustained as part of a stationary subgame-perfect Nash equilibrium if players are sufficiently

patient. Proof. See section 7.3.3.

In this equilibrium, each player gets a share of the total payoffs commensurate with its

power. Any deviation would bring a short-term gain, say if H steals part of the surplus, and

long-term losses, given the grim-trigger strategy of reverting to the inefficient MPE where

war obtains in every period, unless a state is defeated. If players are sufficiently patient, the

short-term gain is outweighed by the long-term losses.

Second assume that there are dynamic consequences to peace, f(κt, st) is strictly increas-

ing in st. Then we can show:

28A stationary subgame-perfect equilibrium is such that, along the equilibrium path, H and C agree on atransfer T (κt) that is solely a function of C’s capabilities at time t, C chooses the efficient level of investmentbe and H does not capture the market.

40

Lemma 9 In the infinite-horizon game where there are dynamic consequences to peace (i.e.

f(κt, st) is strictly increasing in st) and efficient peace would lead to an increase in the

capabilities of the challenger in some period (i.e. f(κt, S(be)(1 + σ)) > κt for some t), then

there is a value for the effectiveness of war N such that if N > N , then war ensues. Proof.

See section 7.3.3.

Intuitively, in any subgame-perfect equilibrium, each country should get a share of the

efficient aggregate surplus that is commensurate with its relative power. For example, C

would prefer going to war than accepting a share of the surplus that is too low, relative to

its capabilities. Yet if efficiency means that C’s capabilities would increase, then H would be

tempted to capture the surplus so as to prevent an increase in C’s capabilities. A necessary

condition for peace is that the increase in the capabilities of C, if H does not capture the

surplus, is less than the cost of war, i.e.

(p(f(κt, S(be)(1 + σ)))− p(κt))UW,V <1− δ

1− δN+1(cC + cH) (6)

When players are sufficiently patient (as δ goes to 1), the right-hand side of the above

inequality converges to cC+cHN+1

, which converges to zero asN goes to infinity, and the inequality

is certain to fail. Put differently, the fact that war is costly allows for the possibility of peace.

However, as the effectiveness of war N increases, then the value of this saving becomes

negligible, and is dominated by the increase in the share of the efficient aggregate surplus

that H would obtain under the current capabilities. Peace unravels. Anticipating that H

would capture the surplus, C’s investment is sub-optimal, peace is inefficient, and war is

likely to ensue.

7.3 Robustness and Extensions: Proof of the Results

Here we present the proof of the results presented in the previous section.

41

7.3.1 Exogenous Power Shifts and War

Proof. (Proof of lemma 5) Strategies in each period are as described in lemmas 1 to 4.

In period 2, whether or not war occurred in period 1, the timing is as described in section

4.1. Therefore, in period 2, the game is played as described in lemmas 1 to 4. Moving up,

the game in period 1 is played in lemmas 1 to 4 since strategies in period 1 have no effect on

period 2. For example, if H captures the market and makes an offer to C, then C accepts if

and only if

z1 + δEUP,C ≥ p(κ1)S(b1)(1 + σ1)− cC + δEUP,C (7)

where EUP,C is C’s expected payoff at the start of period 2, given the possible values

for σ2 and kc,2. The values EUP,C cancel out and we obtain the same condition as in the

one-period game.

Therefore, war happens in period 1 if and only if the cost of capture is low, the value of

externalities is high, and the inefficiency of peace is greater than the cost of war. Since the

inefficiency of peace is decreasing in κt, we have that if condition (1) fails for κ2, then so it

fails for κ1 < κ2.

7.3.2 The Choice Between Guns and Butter

Proof. (Proof of lemma 6). Let us first consider the optimal choice of guns and butter,

assuming that C chooses to produce a strictly positive level of butter (and receives a strictly

positive share of the surplus it creates). C’s problem is to pick b and g so as to maximize

−kbb−kgg+p(κ+ g)S(b)(1 +σ)− cC . This objective function is strictly concave if p′′(.) < 0,

S ′′(.) < 0, and p′′(.)/p′(.)p′(.)/p(.)

S′′(.)/S′(.)S′(.)/S(.)

> 1. The optimal values of b and g satisfy the first-order

conditions, respectively:

−kb + p(κ+ g)S ′(b)(1 + σ) ≤ 0 (8)

42

−kg + p′(κ+ g)S(b)(1 + σ) ≤ 0 (9)

with complementary slackness condition (i.e. b∗ > 0 if and only if condition (8) holds

with equality; g∗ > 0 if and only if condition (9) holds with equality).

First consider condition (8). Since limb→0S′(b) = ∞, then condition (8) must hold with

equality and b∗ > 0. Also note that b∗ < be since p(.) < 1.

Second consider condition (9). Note first that both first-order conditions are functions of

C’s total capabilities, κ + g. Define κs such that conditions (8) and (9) hold with equality

for g∗ = 0.

If κ < κs, C chooses an investment in guns g∗ = κs−κ and an investment in butter b∗(κs)

such that S ′ (b∗(κs)) = kbp(κs)(1+σ)

. If κ ≥ κs, C chooses an investment in guns g∗ = 0 and an

investment in butter b∗(κ) such that S ′ (b∗(κ)) = kbp(κ)(1+σ)

.

We can verify that κs < κmax, since κs is bounded for any finite σ and κmax is arbitrarily

large.29

Next we compare κmin to κs. We conclude that κs > κmin if and only if

−kg + p′(κmin)S(b∗(κmin))(1 + σ) > 0 (10)

where b∗(κmin) is such that S ′(b∗(κmin)) = kbp(κmin)(1+σ)

. Next note that the left-hand side

of condition (10) is decreasing in kg and increasing in σ. Therefore, for any σ, there is a

value kg(σ) such that condition (10) holds if and only if kg < kg(σ).

Now note that the full problem adds two constraints. H’s offer z must be positive and

sufficiently large that C prefers to choose (b, g) 6= (0, 0) instead of (b, g) = (0, 0). These

conditions are, respectively,

29More precisely, define κ′ such that −kg + p′(κ′)S(be)(1 + σ) = 0. Clearly, κs < κ′ so that a sufficientcondition for κs < κmax is κ′ ≤ κmax.

43

p(κ+ g)S(b)(1 + σ)− cC > 0 (11)

−kbb− kgg + p(κ+ g)S(b)(1 + σ)− cC > 0 (12)

From these conditions, we conclude that C chooses the unconstrained optimum if con-

dition (12) holds at the unconstrained optimum and chooses (b, g) = (0, 0) otherwise. In

addition, we note that if σ is sufficiently large, then condition (12) holds at the uncon-

strained optimum for all values of κ. Indeed, the left-hand side of condition (12), evaluated

at the unconstrained optimum, is increasing in κ and in σ, by the envelope theorem. There-

fore, there is a value σ′ such that if σ > σ′, then condition (12) holds for κ = κmin, and hence

for any κ.

Proof. (Proof of proposition 2). As in the baseline model, we conclude that the following

form equilibrium strategies of H and C’s bargaining over T : H’s strategy is as follows: if

condition (1) holds, then H demands T = TC ; if condition (1) fails, then either H declares

war or demands T > TC . C’s strategy is to accept T if and only if T ≤ TC , where TC is given

by equation (2). The only difference is that expected payoffs after peace UP,C and UP,H take

different values, as we explain below. Expected payoffs after war remain the same as in the

baseline model.

Consider Part (i). Payoffs after peace depend on the cost of capture and the value of

externalities.

First consider the case where the cost of capture is high or the value of externalities is

low, (kc, σ) 6= (k, σ). Then UP,H = 0 and UP,C = UW,V . Therefore, UP,H+UP,C = UW,V +UW,L

and condition (1) holds.

Now consider the case where the cost of capture is low and the value of externalities is

high, i.e. (kc, σ) = (k, σ). For κ ∈ [κmin, κs), we have

44

UP,C = −kbb∗(κs)− kg(κs − κ) + p(κs)S(b∗(κs))(1 + σ)− cC (13)

UP,H = −k + (1− p(κs))S(b∗(κs))(1 + σ) + cC (14)

so that total payoffs after peace are

UP,C + UP,H = −k − kbb∗(κs)− kg(κs − κ) + S(b∗(κs))(1 + σ) (15)

For κ ∈ [κs, κmax], we have

UP,C = −kbb∗(κ) + p(κ)S(b∗(κ))(1 + σ)− cC (16)

UP,H = −k + (1− p(κ))S(b∗(κ))(1 + σ) + cC (17)

so that total payoffs after peace are

UP,C + UP,H = −k − kbb∗(κ) + S(b∗(κ))(1 + σ) (18)

First note that the difference in total payoffs, after war and peace, is strictly positive ∀κ,

i.e. (UW,V + UW,L)− (UP,C + UP,H) > 0 since k > 0, b∗(κ) < be ∀κ, and g∗ ≥ 0.

Second note that the difference in total payoffs, after war and peace, is continuous and

decreasing in κ. Indeed, total payoffs after war are independent of κ. Total payoffs after

peace are continuous and increasing in κ, using the envelope theorem.

For Part (ii), the argument is the same as in the baseline model.

7.3.3 The Infinite-Horizon Game

Proof. (Proof of lemma 7). The value of the stage-game payoffs Uw,i are as follows:

UW,V = −kbbe + S(be)(1 + σ), UW,L = 0, UP,C = −kbb∗(κt) + z(b∗(κt)) and45

UP,H = −k + S(b∗(κt))(1 + σ)− z(b∗(κt)), where z(bt) ∈ (0, S(bt)(1 + σ)) satisfies

z(bt) +δp(f(κt, z(bt)))UW,V

1− δ= p(κt)S(bt)(1 + σ) +

δp(κt)UW,V1− δ

− (1− δ)cC1− δN+1

(19)

and b∗(κt) is such that

S ′(b∗(κt)) =kb

p(κt)(1 + σ)(20)

In this equilibrium, strategies are as follows.

H either declares war or offers T > TC; C accepts any T ≤ TC, where

TC = UP,C − VC(κt) + δVC(f(κt, z(b∗(κt)))) (21)

and

VC(κt) =p(κt)UW,V

1− δ− cC

1− δN+1(22)

If war obtained in period t, in bargaining over T , or in any period t′ < t, then V chooses

be, V does not capture the market and would offer to keep the full surplus, and L would accept

any offer;

If peace prevailed in all periods t′ < t and in period t in bargaining over T , C chooses

bt = b∗(κt); H captures any positive surplus and offers zt = z(bt); C accepts zt if and only if

zt ≥ z(bt).

To see that these form an equilibrium, proceed by backward induction. Given these

strategies, war occurs in every period and the value of the game for C and H are given,

respectively, by equation (22) and

VH(κt) =(1− p(κt))UW,V

1− δ− cH

1− δN+1(23)

If war occurred in period t′ < t or in bargaining over T in period t, then strategies for V46

and L are straightforward.

Now assume that peace prevailed in every t′ < t and in bargaining over T in period t. If

C created a surplus and H captured the market, C accepts zt if and only if

zt + δVC(f(κt, zt)) ≥ p(κt)S(bt)(1 + σ)− cC +δ(1− δN)p(κt)UW,V

1− δ+ δN+1VC(κt) (24)

Note that the left-hand side of the above inequality is strictly increasing in zt. The

inequality holds strictly at zt = S(bt)(1 + σ). Also, the inequality fails at zt = 0 if σ is

sufficiently large. Therefore, there is a value σ′ such that if σ > σ′, then C accepts zt if and

only if zt ≥ z(bt), where z(bt) ∈ (0, S(bt)(1 + σ)) and is given in equation (19).

Next observe that H prefers to have an offer zt be accepted rather than rejected if and

only if

S(bt)(1+σ)−zt+δVH(f(κt, zt)) ≥ (1−p(κt))S(bt)(1+σ)−cH+δ(1− δN)(1− p(κt))UW,V

1− δ+δN+1VH(κt)

(25)

Inspecting conditions (24) and (25), we can verify that H strictly prefers to have offer

z(bt) be accepted rather than rejected, since war is costly.

Moving up, consider H’s capture decision. H prefers to capture the surplus if and only

if k < S(bt)(1 + σ) − z(bt) + δ[VH(f(κt, z(bt))) − VH(f(κt, S(bt)(1 + σ)))]. The right-hand

side of this inequality is strictly increasing in σ. Therefore, there is a value σ′ such that H

prefers to capture the surplus if σ > σ′.

Now consider C’s investment decision. The optimal level of investment, assuming bt > 0,

maximizes −kbbt + z(bt) + δVC(f(κt, z(bt))) or maximizes −kbbt + p(κt)S(bt)(1 + σ), i.e. it

is bt = b∗(κt) as defined in the lemma. If C chooses bt = 0, C gets δVC(κt). The payoff

obtained from b∗(κt) increases more quickly with σ than does the payoff obtained from

bt = 0. Therefore, there exists a value σ′ such that if σ > σ′, then C chooses bt = b∗(κt).47

Moving up, consider H and C’s bargaining over T . A transfer T is acceptable to C if and

only if −T +UP,C + δVC(f(κt, z(b∗(κt)))) ≥ VC(κt) or T ≤ TC , where TC is given in equation

(21). A transfer T is acceptable to H if and only if T +UP,H +δVH(f(κt, z(b∗(κt)))) ≥ VH(κt)

or T ≥ TH , where

TH = −UP,H + VH(κt)− δVH(f(κt, z(b∗(κt)))) (26)

A bargaining range fails to exist, and war breaks out, if TC < TH or if condition (5) holds.

Now note that total payoffs after war and peace are, respectively,

UW,V + UW,L = −kbbe + S(be)(1 + σ) (27)

UP,C + UP,H = −k − kbb∗(κt) + S(b∗(κt))(1 + σ) (28)

Thus, the difference in total payoffs, after war and peace, is strictly positive ∀κ, i.e. the

left-hand side of condition (5) is strictly positive. Moreover, the difference in total payoffs,

after war and peace, is decreasing in κt. Indeed, total payoffs after war are independent of κt.

Total payoffs after peace are increasing in κt since b∗(κt) is increasing in κt and b∗(κt) < be.

Now it is clear that if there are no dynamic consequences to war (N = 0), then condition

(5) reduces to condition (1).

If N = ∞, then there is a value δ′ such that if δ ∈ (δ′, 1), then condition (5) holds for

κmax, and thus for all κt.

Proof. (Proof of lemma 8) Assume that there is an MPE where war obtains in every period,

when both states have military capabilities, i.e. condition (5) is satisfied.

We show that there are values σ′ and δ′ < 1 such that for any σ > σ′ and δ ∈ (δ′, 1),

then the following forms a stationary subgame-perfect Nash equilibrium: Players play the

strategies described below, in period 1 and in every period t > 1 if there has been no deviation

in any previous period t < t′, and players revert to the MPE described in lemma 7 for all48

periods t′ > t if there has been any deviation in period t. Strategies along the equilibrium

path are as follows:

H sets T ∗(κ) ∈ ((1− p(κ))UW,V − (1−δ)cH1−δN+1 , (1− p(κ))UW,V + (1−δ)cC

1−δN+1 ]; C accepts T ∗(κ) and

any T ′ 6= T ∗ if and only if T ′ ≤ TC, where

TC = UP,C − (1− δ)VC(κ) (29)

UP,C = −kbb∗(κ) + z(bt), z(b∗(κ)) is as defined in equation (19), b∗(κ) is as defined in

equation (20), and VC(κ) is as defined in equation (22).

If war obtained in bargaining over T , then strategies are as follows: V chooses be, V does

not capture the market and would offer to keep the full surplus, and L would accept any offer;

If peace prevailed in bargaining over T , then strategies are as follows:

C’s investment is be if there was no deviation in period t and b∗(κ) if there was a deviation

in period t;

H does not capture the market if there was no deviation in period t and H captures the

market and offers zt = z(bt) if there was a deviation in period t;

C accepts an offer zt, when H captures the market, if and only if zt ≥ z(bt).

To prove that these form an equilibrium, we proceed as follows. Consider strategies in

period t if a deviation occurred in period t′ < t. Clearly, no player has a strictly profitable

deviation from the MPE of lemma 7.

Now assume that no deviation occurred in any previous period. If there is a deviation in t

such that war occurs in bargaining of T , then strategies for V and L clearly follow the above.

If peace prevailed in bargaining over T , we solve for equilibrium strategies using backward

induction.

If H does not capture the market in period t, the period ends and payoffs are accrued. If

H captured the market in period t, then players expect the MPE to be played from period

49

t+ 1 onwards. Thus, as shown in the proof of lemma 7, there is a value σ′ such that for any

σ > σ′, then C accepts zt if and only if zt ≥ z(bt), where z(bt) ∈ (0, S(bt)(1 +σ)) and is given

in equation (19).

Moving up, consider H’s decision to capture the surplus.

If there was a deviation in period t, then players expect the MPE to be played from

period t+ 1 onwards. Therefore, as shown in the proof of lemma 7, H prefers to capture the

surplus and offer z(bt) if σ is sufficiently large.

If there was no deviation in period t, then by capturing the market H triggers the MPE

from period t + 1 onwards. Therefore, if H captures the surplus, it would prefer to offer

z(be) if σ is sufficiently large. H prefers not to capture the surplus if and only if δ1−δT

∗(κ) ≥

−k + S(be)(1 + σ)− z(be) + δVH(κ) or

δ(T ∗(κ)−(1−p(κ))UW,V +(1− δ)cH1− δN+1

) ≥ (1−δ)(−k+(1−p(κ))S(be)(1+σ)+(1− δ)cC1− δN+1

) (30)

The right-hand side of the inequality is strictly positive, if σ is sufficiently large, and

tends to zero as δ goes to 1. Therefore, there is a value δ′ such that if δ > δ′, then H does

not capture the surplus if

T ∗(κ) > (1− p(κ))UW,V −(1− δ)cH1− δN+1

(31)

Moving up, consider C’s investment decision.

Assume that there was no deviation in period t, i.e. H offered T ∗(κ) and C accepted. By

choosing the efficient investment be, C gets UW,V + δ1−δ [−T

∗(κ) +UW,V ]. With any deviation,

C triggers the MPE in future periods. If σ is sufficiently large, the best deviation for C is to

choose bt = b∗(κ), in which case C gets −kbb∗(κ) + z(b∗(κ)) + δVC(κ). C prefers to choose

the efficient investment if and only if

50

δ[(1− p(κ))UW,V +(1− δ)cC1− δN+1

− T ∗(κ)] ≥ −(1− δ)[UW,V − (−kbb∗(κ) + z(b∗(κ)))] (32)

The right-hand side of this inequality is negative and tends to zero as δ goes to 1. There-

fore, the condition holds if

T ∗(κ) ≤ (1− p(κ))UW,V +(1− δ)cC1− δN+1

(33)

Assume that there was a deviation in period t, withH offering T ′ 6= T ∗(κ) and C accepting

it. In that case, players expect the MPE to be played from period t+ 1 onwards. Following

the proof of lemma 7, if σ is sufficiently large, then C prefers to choose bt = b∗(κ).

Moving up, consider H and C’s bargaining over T . C prefers accepting T ∗(κ) to declaring

war if and only if−T ∗(κ)+UW,V

1−δ ≥ p(κ)UW,V

1−δ − cC1−δN+1 , which is satisfied if and only if condition

(33) holds. If H deviates and offers T ′, C accepts if and only if T ′ ≤ TC as defined in equation

(29).

Moving up, H prefers offering T ∗(κ) to declaring war if and only if T ∗(κ)1−δ ≥

(1−p(κ))UW,V

1−δ −cH

1−δN+1 , which is implied by condition (31).

H prefers offering T ∗(κ) to TC if and only if T ∗(κ)1−δ ≥ TC−k+S(b∗(κ))(1 +σ)− z(b∗(κ)) +

δVH(κ), which is implied by condition (31), since condition (5) holds.

In sum, there is a stationary subgame-perfect Nash equilibrium where peace and efficiency

prevail if conditions (31) and (33) hold.

Proof. (Proof of lemma 9) Assume that there is a subgame-perfect equilibrium where

peace and efficiency prevails, and there is a period t where efficient peace would lead to an

increase in the capabilities of the challenger (i.e. kt+1 = f(κt, S(be)(1 + σ)) > κt). Write

Tt+1 for the average per-period transfer in this equilibrium from period t + 1 onwards, i.e.

Tt+1 = (1− δ)∑∞

s=1 T∗t+s, where T ∗t+s is the equilibrium transfer in period t+ s.

51

A necessary condition is that C does not deviate to declaring war in period t + 1, i.e.

−Tt+1+UW,V

1−δ ≥ VC(κt+1) or

Tt+1 ≤ (1− p(f(κt, S(be)(1 + σ)))UW,V +(1− δ)cC1− δN+1

(34)

Another necessary condition is that H does not want to capture the surplus in period t,

i.e.

δTt+1

1− δ≥ −k + S(be)(1 + σ)− z(be) + δVH(f(κt, z(b

e))) (35)

where we use the fact that by capturing the surplus, H triggers the MPE and offers z(be)

(if σ is sufficiently large), which C accepts. Rearranging this condition, we get

δ(Tt+1−(1−p(κt))UW,V +(1− δ)cH1− δN+1

) ≥ (1−δ)(−k+(1−p(κt))S(be)(1+σ)+(1− δ)cC1− δN+1

) (36)

The right-hand side of the inequality is strictly positive, if σ is sufficiently large, and

tends to zero as δ goes to 1. Therefore, the inequality is satisfied for δ close to 1 if and only

if

Tt+1 > (1− p(κt))UW,V −(1− δ)cH1− δN+1

(37)

Together, conditions (34) and (37) are compatible only if condition (6) holds. As N tends

to infinity and as δ tends to 1, condition (6) fails, given that f(κt, S(be)(1 + σ)) > κt.

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Figure  1:  Game  Tree  of  the  Baseline  Model  

Nature  chooses  externali;es  σ  and  cost  of  capture  kc  

H  

declares    war  

V  chooses    investment  b  …    

accepts  

demands  T  C  

declares                  war  

V  chooses    Investment  b  …    

C   H  

does  not    capture  

captures,  offers  z  

chooses    investment    b  >0   C  

declares                    war  

accepts  

Note:  Payoffs  are  omiNed  for  simplicity  

chooses                  b=0  

game  ends  

game  ends  

game  ends  

game  ends  

Figure  2:  The  Inefficiency  of  Peace  

Investment  xb  

Surplus  S(xb)  

xb*  

S’(xb)=kb/(1+σ)  

S’(xb)=kb/[p(1+σ)]  

xbe  

Figure  3:    The  Choice  of  Guns  and  BuNer  

κs-­‐κ   g  (Guns)  

b*(κs)  

b  (BuNer)  

g  (Guns)  

b  (BuNer)  

Weak  Challengers  (κ  <  κs)   Strong  Challengers  (κ  ≥  κs)  

kbb  +kgg=k0  

p(κ+g)S(b)(1+σH)=u0  b*(κ)