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On the size and structure of group cooperation

  • Haag, Matthew
  • Lagunoff, Roger

This paper examines characteristics of cooperative behavior in a repeated, n-person, continuous action generalization of a Prisoner's Dilemma game. When time preferences are heterogeneous and bounded away from one, how "much" cooperation can be achieved by an ongoing group? How does group cooperation vary with the group's size and structure? For an arbitrary distribution of discount factors, we characterize the maximal average cooperation (MAC) likelihood of this game. The MAC likelihood is the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, that the group can achieve. The MAC likelihood is shown to be increasing in monotone shifts, and decreasing in mean preserving spreads, of the distribution of discount factors. The latter suggests that more heterogeneous groups are less cooperative on average. Finally, we establish weak conditions under which the MAC likelihood exhibits increasing returns to scale when discounting is heterogeneous. That is, larger groups are more cooperative, on average, than smaller ones. By contrast, when the group has a common discount factor, the MAC likelihood is invariant to group size.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 135 (2007)
Issue (Month): 1 (July)
Pages: 68-89

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Handle: RePEc:eee:jetheo:v:135:y:2007:i:1:p:68-89
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. George J. Mailath & Ichiro Obara & Tadashi Sekiguchi, . "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Penn CARESS Working Papers 83719e84b6825736ffcfdfacb, Penn Economics Department.
  2. Fudenberg, Drew & Levine, David K, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Econometrica, Econometric Society, vol. 57(4), pages 759-78, July.
  3. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
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  5. Marco Celentani, 1993. "Maintaining a Reputation Against A Long-Lived Opponent," Discussion Papers 1075R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November.
  7. Matthew Haag & Roger Lagunoff, 1999. "Social Norms, Local Interaction, and Neighborhood Planning," Game Theory and Information 9907004, EconWPA.
  8. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  9. Harrington, Joseph Jr., 1989. "Collusion among asymmetric firms: The case of different discount factors," International Journal of Industrial Organization, Elsevier, vol. 7(2), pages 289-307, June.
  10. Martin McGuire, 1974. "Group size, group homo-geneity, and the aggregate provision of a pure public good under cournot behavior," Public Choice, Springer, vol. 18(1), pages 107-126, June.
  11. Stahl, Dale II, 1991. "The graph of Prisoners' Dilemma supergame payoffs as a function of the discount factor," Games and Economic Behavior, Elsevier, vol. 3(3), pages 368-384, August.
  12. Pecorino, Paul, 1999. "The effect of group size on public good provision in a repeated game setting," Journal of Public Economics, Elsevier, vol. 72(1), pages 121-134, April.
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