self-enforcing norms and efficient non-cooperative collective action in the provision of public...

Self-enforcing norms and efficient non-cooperative collective

action in the provision of public goods

Kai A. Konrad and Wolfgang Leininger

Edinburgh, May 16, 2008

How to motivate the members of a group to contribute to the group specific public good?

How to solve the distributional conflict within the group?

We study how these problems interact, and how one problem can solve the other.

Collective goods problems in groups

Contributions to collective group effort

yj

Group N

Group members j





Internal conflict about

distribution

xj

Group N

Group members j





Contributions to collective group effort

Internal conflict about

distribution

xj

yj

Group N

Group members j

The framework explains how both problems can be solved non-cooperatively.

Non-cooperative provision of a pure public good Bergstrom, Blume and Varian (1986)Andreoni (1990) Bagwell and Bernheim (1996) Glazer and Konrad (1996) Bénabou and Tirole (2006)

Inter-group and intra-group conflict Nitzan (1991) Davis and Reilly (1999) Katz and Tokatlidu (1996) Wärneryd (1998) Müller and Wärneryd (2001)

Why is the message of this paper important?

Production and appropriation in the absence of the enforcement of property rights Skaperdas (1992) Hirshleifer (1988, 1995) Grossman (1994)

Enforcement power and its self-constraints Olson (1993) McGuire and Olson (1996) Skaperdas (2002)

Collective choice on the adoption of an enforcement technologyFalkinger (2006) Sánchez-Pagés and Straub (2006) Gradstein (2007)

Related literature

Ni = 1

i = 2

i = 3

The clan

Set N with n members. Member i = 1 is called “the leader”.

External enemy

?Ey

y1

y2

y3

Stage 1: Fighting the external enemy

Clan fights with an external enemy for a prize of size V = 1. Each group member i chooses own fighting effort. Group effort is the sum of individual efforts.

1

.n

C jj

y y

1

.n

C jj

y y

a2

a3

„Leader“

a ≡ (a2 , a3 , ... , an)

with ai ≥ 0

Stage 2: Donations to clan members

The clan leader chooses a set of payments

21 1 1 1 1 1( ,..., ) ( )njn jy p x x V a C x

1( ,..., ) ( )j j j n j j jy p x x V a C x

All i chooset { e, l }.

e l

2

j

j j

x

c x 2

k

k k

x

c x

The highest xi wins.

for j ≥ 2

Internal conflict

The mechanism is empirically relevant.

Example 1: Melanesian tribes

Example 2: The Palestinian Liberation Organization (PLO)

Example 3: Modern investment banking


Orenstein et al. (1980, p. 71):In this kind of ideology the leader is thought to give by right and receive by grace. The ordinary people, having elevated one of their members to the superordinate place, hold him in their debt for this honor and require him to supply their expressed needs. What the leader gives to his constituency is their due; what he gets from them – largely the honor of high office – is by their grace.

This mutual giving has often been interpreted as reciprocating behavior (Sahlins 1963, p. 293). Our non-cooperative approach reveals that what looks like mutual exchange or reciprocity from the outside may be a sequence of actions in a subgame perfect equilibrium among narrowly selfish players.

Sahlins (1963, p. 293): also reports that “... there are not merely instances of big-man chicanery and of material deprivation of the faction in the interests of renown, but some also of overloading of social relations with followers: the generation of antagonism, defections, and in extreme cases the violent liquidation of the center-man.”

Orenstein et al. (1980, p. 72), referring to several other sources, reports:“Revolutions,” usually bloodless, are frequent, for the people stand to gain from the installation of a new headman – that is, from the new man's as yet unconstrained resources.

Examples (1): The big-man in Melanesian tribes (Sahlins 1963, Orenstein et al. 1980)

Livingstone and Halevy (1990, pp. 184-185):Money is the source of Yasir Arafat’s power. Without it Arafat would have been just another voice in the tumult, another salesman of broken dreams, a kind of Palestinian Willi Loman. Instead, he is a global mover and shaker, feted by kings and prime ministers, the leader of a revolution that threatens to change the map of the world. He is feared by his enemies, who know that his threats are not hollow, and loved by his followers, who know that he can be a generous patron.

Examples (2): Yassir Arafat, the PLO and the Chairman's Secret Fund

Knee (2007, p. 120): The problems of incentives for making business and for installing merit based compensation:

“... any other alternative would have resulted in fistfights between bankers in the hallways, there was not even a theoretical limit to how many bankers could claim credit for the same deal.”

William D. Cohan (2007, pp. 182n.): Michel was generally happy to reward his partners well, often better than they could possibly be paid by other firms. He was long-term greedy and knew that if the pie kept getting bigger, he stood to make more money himself, as he had the largest profit percentage by far. Mostly, though, Michel was interested in his partners' ability to generate fees - as he himself had little ability or desire to do so.

Examples (3): Investment banking as an example for the “modern cooperation”

Clan: Set N with n members. Member i = 1 is called “the leader”.

Stage 1: Clan fights with an external enemy for a prize of size V = 1. Each group member i chooses own fighting effort, yi.

Group effort y is the sum of yi. The prize is awarded to the group that expends the

higher sum of efforts.

Stage 2: The clan leader chooses a set of payments (a2, ... ,an),

with aj ≥ 0 the payment made to j N.

Stage 3a-c: Internal conflict. All clan members enter into an all-pay auction with endogenous timing.

Stage 3a: Each clan member chooses his timing of expending intra- group effort: early (at time e), or late (at time l).

Stage 3b: All clan members i who chose time e expend their intra-group efforts xi ≥ 0.

Stage 3c: All clan members i who chose time l expend their intra-group efforts xi ≥ 0.

The analytical framework

Who wins the intra-group contest? pi (x1, … ,xn)

Effort cost: Ci (xi ) = ci xi ² with c1 ≤ c2 ≤ ... ≤ cn .

Overall payoffs if the group wins the prize:

“big man”’s payoff:

Ordinary group member’s payoff:

The analytical framework

21 1 1 1 1 1( ,..., ) ( ).njn jy p x x V a C x

1( ,..., ) ( ).i i i n i i iy p x x V a C x

The first main result

For any a , there exists a subgame perfect equilibrium of the continuation game in stages 2-3c, in which player 1 chooses a at stage 2, player 1 chooses l and all other players j choose e, and xj = 0.

1

222

{ ( ,..., )| and 0 for 2,..., }.n

cn j jc

j

a a a a j n

a

The vector of gifts

Wasteful conflict equilibrium

y ≠ y*

(y1 , y2, ... , yn)Peaceful equilibrium

t1 = l

tj = e, for all j ≥ 2

xi = 0, for all i.

a ≠ a*

y = y*

a = a*

a = ( a2, ... , an)

t1 = … = tn = l

Competition (all-pay contest) between the clan and an enemy for a prize valued V = 1.

The enemy's cost of effort

Each clan member's effort contribution: yj .

Cost of this effort contribution:

Total clan effort

The clan wins if yC > yE.

Collective action (stage 1)

* 2( ) .E E E ED y c y

2( ) .j j j jD y c y

1

.n

C jj

y y

The cost-minimizing way to generate yC for n = 3 with:

2

11

1( ) with .

j

C nj c

D y cy c

1 1( )C y

1y

1y

2y

2y*1y *

2y

2 2( )C y

*1 1'( )C y

1 1'( )C y 2 2'( )C y

1 1( )C y

3 3'( )C y

3y

2 2( )C y 3 3( )C y

3y*3y

3 3( )C y

1 1'( )C y 2 2'( )C y 3 3'( )C y

The clan’s equilibrium payoff if the collective action problem is managed efficiently:

The condition cE > c defines potential superiority of the clan.

max{1 ,0}.CE

cc

Second main result

Let the clan be potentially superior to the enemy in the sense of (cE > c). If c1 – c2 is sufficiently close to zero, then a subgame perfect equilibrium exists in which the clan can implement the externally efficient efforts and a peaceful distribution of rents from external conflict.

Equilibrium collective action

Comparative static properties:

Let cj = c0 for all j.

A sufficiently large clan exists such that cE > c if

0

11

1lim ( ) lim 0.

nn nj c

c n

Let all clan members have the same ci = c0 :

The number of clan members that maximizes the individual member's payoff in the efficient equilibrium is described by

Optimal egalitarian clan size

02 .E

cn

c

The potential intra-group redistributional conflict can solve the free-rider problem inside the group and yield full efficiency.

A “norm” governs the equilibrium path that is chosen, and fear about a possible continuation path reinforce the norm.

Conclusions

The mechanism that causes this looks like reciprocity, but isn’t.

There is no reciprocity, no altruism, no inequality aversion, no enforcement agency, just fear about another possible equilibrium.

Conclusions

Reciprocity?

Group membersgive contributions

to group effort.

Big-man hands out gifts to

group members.

If the contributions or the gifts are

insufficient, they end up fighting.

Reciprocity?

Punishment?

THE END

self-enforcing norms and efficient non-cooperative collective action in the provision of public...

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