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On the Size and Structure of Group Cooperation

  • Matthew Haag

    (University of Warwick)

  • Roger Lagunoff

    (Georgetown University)

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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File URL: http://econwpa.repec.org/eps/game/papers/0209/0209005.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0209005.

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Length: 31 pages
Date of creation: 30 Sep 2002
Date of revision:
Handle: RePEc:wpa:wuwpga:0209005
Note: Type of Document - pdf; prepared on PC; to print on postscript; pages: 31 ; figures: included ;
Contact details of provider: Web page: http://econwpa.repec.org

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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. Drew Fudenberg & David K. Levine, 1995. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 103, David K. Levine.
  3. 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.
  4. 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.
  5. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
  6. Matthew Haag & Roger Lagunoff, 2006. "Social Norms, Local Interaction, And Neighborhood Planning ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(1), pages 265-296, 02.
  7. 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.
  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. D. Fudenberg & D. M. Kreps & E. Maskin, 1998. "Repeated Games with Long-run and Short-run Players," Levine's Working Paper Archive 608, David K. Levine.
  10. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November.
  11. 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.
  12. 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.
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