rent-seeking, rent-defending, and rent dissipation

Public Choice 71: 61-70, 1991. © 1991 Kluwer Academic Publishers. Printed in the Netherlands.

Rent-seeking, rent-defending, and rent dissipation*

CHRIS PAUL AL WILHITE Department of Economics, University of Alabama in Huntsville, Huntsville, AL 35899

Submitted 24 December 1989; accepted 16 March 1990

1. Introduction

A substantial portion of the research on rent-seeking addresses the issue of rent dissipation. This line of inquiry is drawn directly from Tullock's (1967) stated intent to identify the total social costs of monopoly. Early studies, which were concerned with the measurement of Tullock costs, simply assumed dissipation would be complete (see Becker, 1968; Kruger, 1974; Posner, 1975; and others). However, Posner (1975) and Fisher (1985) observed the question of dissipation can be answered only for overtly specified game structures.

Tullock (1980) and Rogerson (1982) introduced a rent-seeking game which yielded incomplete dissipation under a wide variety of cost conditions. In spite of Tullock's suggestion that the incomplete-dissipation result might be the more interesting, several authors responded by introducing variations of the game in attempts to obtain a general complete dissipation result (see Corcoran, 1984; Corcoran and Karels, 1985; Higgins, Shugart and Tollison, 1985; and Tullock's responses, 1984, 1985 and 1987).

Along similar lines, several authors have considered necessary conditions for excess dissipation. Lott (1987) argues that non-transferable licenses yield this result. However, Gahvavi (1989) has questioned his conclusion. Additionally, Toliison (1989) has posited the occurrence of excess dissipation when the rent seeker can generate extra-game revenue as a result of insider information generated by participation in the rent-seeking game.

Wenders (1987) addressed the social costs of rent-seeking to obtain a monopoly and concludes, "recurring or sunk, even the largest specification of the Harberger and Tullock costs of regulation may fall f a r short of the actual welfare costs. This is because the analysis concentrates on the rent-seeking Tullock costs and largely ignores the parallel rent-defending Tullock costs" (Wenders, 1987: 456, emphasis in original). Wenders is concerned with situations in which

* The authors wish to thank Randall Holcomb, Philip Porter, William Shugart and Gordon Tul- lock for helpful comments on an earlier version. Naturally remaining errors are the responsibility of the authors.

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P

T

Qm Qc Q Figure 1. Competitive prices and outputs are subscripted c, and m is used for monopolies

welfare losses are larger than the sum of the Tullock rectangle (T) and Har- berger triangle (H), shown in Figure 1. While he raises some interesting issues, his analysis is often incomplete and his conclusions misleading. This paper more fully develops some of these topics and presents conclusions that have not

appeared in the literature.

2. Rent-seeking and rent-defending

Wenders initially consider instances of binary regulation in which the regulated price is set at either the monopoly, Pro' or the competitive, Pc, level. Adopting Posner 's (1975) assumption that competition for monopoly power will trans- form all expected rents into welfare losses, Wenders (1987: 457) observes, " there are parallel activities and resource expenditures by those who stand to lose from restrictive regulations as they seek to defend against rent-seeking activities." Then, invoking a prisoners' dilemma mechanism, Wenders concludes dissipation is up to twice the level suggested by the traditional Tullock and Har- berger costs. He writes (Wenders, 1987: 458), "why would the sum of rent- seeking and rent-defending expenditures exceed T + H? The answer lies in an analysis similar to the prisoner's dilemma theory (Magee, 1984: 47-48). Like the prisoners who both confess, neither buyers nor sellers may refrain from spending the maximum amount they each have at s take." However, Wenders fails to demonstrate how the analysis of domestic regulation presented in his paper is "s imilar" to the model constructed by Magee. A review of the Magee-

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Young model shows it applies to a substantially different situation than the

case forwarded by WendersJ The Magee-Young (1984) model is specifically formulated to represent possi-

ble outcomes of trade policy with resulting assumptions that are inappropriately applied to the incorporation of rent-defending expenditures in the regulation of a domestic industry. In the Magee-Young model all participants are owners of labor or capital and while they can choose to stay out of rent-seeking activities, they cannot escape the ramifications of its outcome; short of migrating to another country. However, in the regulation of a single domestic industry,

which is Wenders' example, both resource suppliers and consumers are able to exit the rent-seeking competition and its consequences. Producers can transfer capital to competing uses and consumers can find substitutes or move to a dis- tinct regulatory environment. Thus, seekers' ability to enter and exit the rent- seeking game nullifies the prisoner's dilemma argument posited by Wenders (see Higgins, Shughart and Tollison, 1985; and Corcoran and Karels, 1985).

Furthermore, the results cited by Wenders are interpretively different than those cited by Magee. In a single market, behavior which results in both consumers and producers being worse off requires excess dissipation of available rents or consumer surplus. However, the Magee-Young model is one of factor payments. Factor owners attempt to increase the payment per unit of resource by imposing either a subsidy on an exported good or a tariff on an imported good. Under this two factor construct both groups can be worse off, but this does not imply excess dissipation. Under the Magee-Young model, dissipation is limited to 100 percent of available rents.

2.1. The Posner model

While Wenders inappropriately applies the Magee and Young prisoners' dilem-

ma mechanism, rent defending has some interesting welfare implications, but specific implications depend on the type of rent-seeking model employed. Wenders adopts Posner 's (1975: 76) construct by assuming rent seekers bid the expected value of the transfer. In Posner 's example, if ten risk-neutral firms have an equal chance of capturing a monopoly with a present value of $1,000~000, each will spend $100,000. The rent is completely dissipated. As- suming consumers are organized and capable of raising and spending an amount equal to producers, 2 the probability of monopoly pricing falls from 1

, to .5, and the expected value of the Posner game for any one of ten producers becomes 0.1 (.5($1,000,000)) = $50,000. The total expenditure of the organized consumer group is 0.5($1,000,000) = $500,000. Expenditures by rent- seeking producers and rent-defending expenditures by consumers sum to the rent value of $1,000,000. Dissipation is still complete but not excessive. 3

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To assess rent-seeking costs, the rent at stake must be identified and the model formalizing these activities selected. In the monopoly pricing case, rent- defending consumers behave similarly to rent-seeking producers because the stake for which they are competing is the same: the property right to set prices. If the right is won by producers, prices increase to the monopoly level. If consumers win, prices remain at the competitive level. Consumers may well be in- terested in defending the competitive price, but the return to their rent- defending expenditures is affected by their probability of winning. Wenders reached an excess-dissipation conclusion by failing to explicitly formulate the impact of consumer participation on the expected value of the contested rents. 4

2.2. The Tullock-Rogerson model

As previously noted, a strategic game model of rent-seeking behavior has been posited by Tullock (1980) and Rogerson (1982). They envision seekers who in- fluence the probability of winning by investing increasing sums in the game. With two identical risk-neutral players, A and B, the expected value of rent- seeking for player A is,

a E(a) - - - (T) - a, (1)

a + b

where " a " represents A's rent-seeking expenditures, " b " is B's expenditures and T is the rent at stake. Player A maximizes the expected value, and the optimal bid, a*, depends on B's effort and the rent at stake.

a* = - b + ~ (2)

B faces an identical choice and generates a similar reaction function. As each player responds in turn, a Cournot-Nash-type equilibrium is attained where each player bids 1/4 of the rent value. With n players the equilibrium investment by A is aeq = [ ( n - 1)/n 2] T. 5

Now, suppose consumers, or any party currently holding the property right to this pricing power, engage in rent-defending activities. This formulation merely changes equation (1) for the rent defender by transforming the rent to a negative value. Specifically, the defender is now competing to maintain the rent. Make player A the rent seeker and player B the rent defender. While A's expected value calculation remains unchanged B's expected value becomes,

a E(b) - - - ( - T ) - b . (3)

a + b

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B's expected value is negative. If B's rent defense is unsuccessful, all previously controlled rent is lost, while a successful defense reduces the defender's wealth by the amount of the expenditure. Solving for B's optimal response function, b*, yields,

b* = - a + x /aT; (4)

a* is given by equation (2). If both players maximize their expected value the equilibrium solutions is un-

changed from the simple two-player game with aeq = (1/4)T and beq = (1/4) T. The total rent-seeking investment remains (1/2)T. 6 The equilibrium level of rent dissipation is unchanged. 7

3. Nested games

Wenders speculatively offers another reason for excess dissipation based on successive rounds of rent-seeking. His example involves consumer groups united against a utility rate increase. Once a new rate is established inviduals compete among themselves to deflect the increase to others. As he eloquently states (1987: 457), "Lions and wolves cooperate in the hunt but scrap over the kill."

3.1. The Posner model

The issue of multi-stage or nested games is an interesting one, but again specific results depend on the model applied. Consider a two-stage Posner expected value game in which ten rent seekers pursuing a $1,000,000 prize are divided into two groups consisting of five cooperative consumers and five united producers. The first stage of the game determines which group controls the property right; the second stage assigns the rent value to a member of the winning coalition. Players are allowed to rebid at the beginning of each stage, s Stage one is worth 1/2[(1/5) $1,000,000] = $100,000 for each of ten players, and stage two is valued at 1/5($1,000,000) -- $200,000 for the remaining five players. It appears twice the rent value is spend in the game. But, how useful is this result?

The total expected value for each player is a negative $100,000. 9 Thus, a ra- tional wealth-maximizing player would not voluntarily participate in this game. Furthermore, if one player decides to withdraw from the coalition and compete alone, the single player's potential winnings is (1/3)($1,000,000). The value to the competing teams is adjusted accordingly. The independent player

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is now breaking even, with an expected value equal to zero, while players in the coalitions continue to incur losses. 10 More importantly, all players benefit by leaving their collusive arrangements and competing independently.

This result arises because of the nature of the Posner model. The chance of an individual acquiring a monopoly right is determined by the number of bids. The award is randomly assigned. Rent-seeking expenditures are then assumed to be equal to the wager making a risk-neutral person indifferent between playing and not playing. The distinctive characteristic of the Posner model is the level o f expenditures a person commits does not affect their probability o f at- taining the rent) 1 Hence, joining a coalition is not a maximizing decision, because collusive rent-seeking is costly but has no impact on the individual's probability of winning.

3.2. The Tullock-Rogerson model

The Tullock-Rogerson model allows additional expenditures to affect the probability of winning, hence collusive agreements can be wealth enhancing. 12 For example, suppose there are four identical risk-neutral seekers, A, B, C, and D. Playing independently, each will invest [(n- l)/n2]T = (3/16)T leading to aggregate dissipation of 3/4(T). Consider the formation of two coalitions, consisting of players A and B versus players C and D, who collude for the first game and compete if the first round is successful. Coalitions face two crucial decisions: (i) how to distribute first-round rent-seeking costs among members?; and (ii) how to divide profits of a win?. If these distribution questions can be settled by a pregame agreement, coalition rent-seeking is no different than games with individual players, excepting contracting and enforcement costs.

There are many instances in which this is not the case. Suppose the benefits of a successful first round of rent-seeking benefits a particular individual regardless of participation in the game. This non-excludability problem will make it difficult for the coalition to garner sufficient resources for the first round. Many, perhaps all, the beneficiaries will prefer to be free riders. Many consumer issues are of this type, and the free-rider problem may severly restrict coalition formation.

If, however, the profits of the first round of rent-seeking can be restricted to the coalition members, the question of allocating costs can be solved. Each member's willingness to pay is determined by their proportional benefit, and costs can be allocated through some traditional bargaining mechanism. However, profit distribution is still an issue. This problem of distributing first- round profits initiates a second round of rent-seeking.

Suppose two coalitions, a consisting of players A and B and/3 consisting of players C and D, are placed in this situation. As discussed above, the value of

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the second game is (1/4)T and so the expected value of this game for coalition is:

O/ E (a) - - - (.25T) - a, (5)

c ~ + ~

where a = a + b and/3 = c + d. That is, c¢ and j3 represent the combined investment of coalitions consisting of players A and B and players C and D, respectively. The optimal strategy for a coalition is identical to the reaction function of the two-person game given in equation (2), but the rent at stake in the first round is only (1/4)T. The cost of competing in the first round is p(1/4) (1/4 T) = p(1/16)T for player A, and (1 - p ) (1/4) (1/4)T = (1 - p ) (1/16)T for B, where p and (1 - p) represent A and B's share of the first round expenditures. With the j3 coalition facing the same decision aggregate rent-seeking costs of the initial round equals (1/8)T. Second-round expenditures remain (1/2)T. With coalitions aggregate rent-seeking costs have declined to (1/8)T + (1/2)T = (5/8)T from the sum of (3/4)T in the single-stage rent-seeking game. However, this reduction does not account for coalition formation and enforcement costs.

Aggregate rent-seeking expenditures are lower in the coalition rent-seeking structure, but this result is interesting only if these collusive agreements pay. In other words, each player must be better off, or at least indifferent to the formation of coalitions. This is verified by calculating the expected value of each game for a single player. With four identical players participating in a single- stage game each player has a 1/4 chance to win T - (3/16)T and 3/4 chance to win - (3/16)T. The expected value for player A in the first game is, E(a)l = (1/4) ( T - (3/16)T) + (3/4) ( O - (3/16)T) = (1/16)T. In a two-stage game, returns differ depending on the result of the first game, A's expected value becomes, E(a)2 -- (1/4) ( T - ( 9 / 3 2 ) T ) + (1/4) ( O - ( 9 / 3 2 ) T ) + (1/2) ( O - ( 1 / 32)T) = (3/32)T. The nested game yields a (1/32)T gain over the single-stage game for each of these identical players.

If rent can be restricted to identifiable participants with players facing identical choices, there is an incentive for coalitions to form and nested, two-stage, games to arise. More importantly, the creation of nested games can reduce aggregate welfare losses attributable to rent seeking. However, the reduction in rent-seeking expenditures will to some extent be negated by the costs associated with coalition formation and enforcement. While potential coalitions may be stifled by free-rider problems and organizational costs, rent-seeking coalitions do exist; Wenders gives examples. And, it is intuitively pleasing to find a model suggesting their existence is wealth maximizing.

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4. Summary and conclusions

In the preceding analyses o f ren t -defending , the Posner mode l y ie lded welfare

losses in excess o f the c o m b i n e d areas o f the Tul lock rectangle and the Ha r -

berger t r iangle in on ly one instance. F u r t h e r m o r e , this pa r t i cu la r c i rcumstance

necess i ta ted vo lun t a ry pa r t i c ipa t ion in a game with a negat ive expected

value. 13 F o r the Tu l lock -Roge r son model , the explicit add i t i on o f rent-

defenders h a d no impac t on aggregate d iss ipa t ion .

In add i t ion , this p a p e r in t roduced two impl ica t ions o f nested games on rent-

seeking theory . Firs t , in cases where the Posner expected value b id appl ies , coa-

l i t ions will no t fo rm. Second , coa l i t ions arise as a resul t o f wea l th -maximiz ing

behav io r in the T u l l o c k - R o g e r s o n s t ra tegic game, bu t c o n t r a r y to previous

au thors this mode l suggests, rent-seeking expendi tu res fall. However , the or-

gan iza t iona l and enfo rcement costs o f coa l i t ions reduces the wel fare gain and

under some c i rcumstances m a y negate the gains to coa l i t ion fo rma t ion .

There seem to be two c o m m o n pi t fal ls in the analysis o f welfare costs o f rent-

seeking activit ies. F i rs t , the rent at s take is of ten incorrec t ly ident i f ied . Second,

the m e t h o d used to a l locate rents, o r the s t ructure o f the game, is not expl ici t ly

fo rmula t ed . Viewing rent as claims to p rope r ty r ights should help al leviate the

p rob lems ar is ing f rom the fo rmer , and cont inu ing research into a l ternat ive

rent-seeking models represents a m o v e m e n t t o w a r d the la t ter . 14

Notes

1. The Magee paper cited by Wenders is a secondary source which contains neither a model nor description of the prisoners' dilemma application. However, a citation within that paper, Ma- gee and Young (1982), contains their model and analysis. The version supplied to us by Magee and cited herein is a later version dated 1984.

2. There are several problems with this assumption including the public good characteristic of non-exclusion (see Ursprung, 1989), and the differing organizational costs of consumers and producers.

3. An alternative approach would be to include a consumer coalition as an additional competitor to the ten firms. Under this formulation the expected value for all competitors is (I/11) T and the perfect dissipation result is unchanged. Curiously, if Wenders logic is accepted, i.e., all players bid the rent at stake, total dissipation would equal $11,000,000, but even Wenders does not suggest this magnitude of shortsightedness. Why are consumers less able to adjust for competition than producers? Why do producers adjust their bid to one type of competitor but not another?

4. Using a general equilibrium model, DeLorme and Snow (forthcoming) reach a similar conclusion. Specifically, they show rent-avoidance typically reduces social waste and dissipation is less than the Harberger-Tullock trapazoid as long as rent-seeking and/or rent-defending is not subsidized by the government.

5. More recently Tullock (1987) argues social losses will be higher than the efficient rent-seeking model suggests, but those issues lie outside this discussion.

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6. In cases where the rent-defender is a coalition of consumers defending the competitive price, they have an additional stake equal to the value of the Harberger triangle. Their expected value

is similar to equation (3) with T ' = T + H substituted for T. 7. The foregoing analysis implicitly assumes producers' and consumers' expenditures are equally

efficient in changing the probability of capturing the monopoly rent. However, if there is a bias, say in favor of existing property rights, the magnitude of dissipation would be reduced

further. 8. Some interesting arrangements are omitted. For example, coalitions could negotiate contracts

defining the proportion of expenditures provided by each member of the team and rules governing the distribution of the rent if their coalition wins. Or, the rules of the game could limit all bids to the beginning (no bids in stage two). In these cases Posner 's original conclusion

holds. 9. Wenders claims his essay points to excess dissipation for costs that are either recurring or sunk.

Not only do bidders play negative sum games, but they do so repeatedly. 10. Total dissipation also differs. If the independent player wins the first round, there is full dissi-

pation as no expenditure occurs in round two. Double dissipation occurs only when the first

round is won by a coalition. 11. Naturally, a person could play twice, but each bid is an independent decision. 12. There are several interesting ways to formulate two-stage games and many yield unique results.

Unfortunately, a comprehensive review would lead us far astray. The case explored here was selected because it seemed to be in line with Wenders' thinking.

13. Tollison's (1989) "superdissipation" appears to be a viable theory for excess dissipation. 14. For example, Hillman and Riley (1989) and Paul and Wilhite (1990) present several rent-

seeking structures applicable to a variety of situations.

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rent-seeking, rent-defending, and rent dissipation

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