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On the Size and Structure of Group Cooperation

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  • Matthew Haag

    (Department of Economics, University of Warwick)

  • Roger Lagunoff

    (Department of Economics, Georgetown University)

Abstract

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 co-operation (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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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2003.54.

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Date of creation: Jun 2003
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Handle: RePEc:fem:femwpa:2003.54

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Keywords: Repeated games; Maximal average Cooperation likelihood; Heterogeneous discount factors; Returns to scale;

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  1. Fudenberg, Drew & Kreps, David M & Maskin, Eric S, 1990. "Repeated Games with Long-run and Short-run Players," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 555-73, October.
  2. Matthew Haag & Roger Lagunoff, 1999. "Social Norms, Local Interaction, and Neighborhood Planning," Game Theory and Information 9907004, EconWPA.
  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. 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.
  5. Drew Fudenberg & David Levine, 1987. "Reputation and Equilibrium Selection in Games With a Patient Player," Working papers 461, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. 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.
  7. Mailath, George J. & Obara, Ichiro & Sekiguchi, Tadashi, 2002. "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 40(1), pages 99-122, July.
  8. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November.
  9. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
  10. 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.
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Cited by:
  1. Alexander E. Saak, 2012. "Collective Reputation, Social Norms, and Participation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(3), pages 763-785.
  2. Paul Pecorino & Akram Temimi, 2007. "Public good provision in a repeated game: The role of small fixed costs of participation," Public Choice, Springer, vol. 130(3), pages 337-346, March.
  3. Wiktor Adamowicz & Michel Hanemann & Joffre Swait & Reed Johnson & David Layton & Michel Regenwetter & Torsten Reimer & Robert Sorkin, 2005. "Decision Strategy and Structure in Households: A “Groups” Perspective," Marketing Letters, Springer, vol. 16(3), pages 387-399, December.
  4. Andrea Galeotti & Miguel Mel�ndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute.
  5. Juan Escobar, 2008. "Cooperation and Self-Governance in Heterogeneous Communities," Discussion Papers 07-038, Stanford Institute for Economic Policy Research.
  6. Andrea Galeotti & Miguel Mel�ndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute.
  7. Elias Asproudis, 2011. "Revisiting environmental groups and members’ behaviour: budget, size and (im)pure altruism," Environmental Economics and Policy Studies, Society for Environmental Economics and Policy Studies - SEEPS, vol. 13(2), pages 139-156, June.
  8. Roger Lagunoff & Matthew Haag, 2002. "One Size and Structure of Group Cooperation," Working Papers gueconwpa~02-02-05, Georgetown University, Department of Economics.
  9. Fon, Vincy & Parisi, Francesco, 2008. "Role-reversibility, stochastic ignorance, and social cooperation," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(3), pages 1061-1075, June.
  10. Bowen, T. Renee & Zahran, Zaki, 2009. "On Dynamic Compromise," Research Papers 2020, Stanford University, Graduate School of Business.

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