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On the Size and Structure of Group Cooperation

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Author Info

  • Matthew Haag

    (University of Warwick)

  • Roger Lagunoff

    (Geogetown 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 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, in the group. We show that the MAC likelihood is increasing in monotone shifts, and decreasing in mean preserving spreads, of the distribution of discount factors. This suggests that more heterogeneous groups are less cooperative. Finally, we show under certain conditions that the MAC likelihood exhibits increasing returns to scale when discounting is heterogeneous: larger groups are more cooperative than smaller ones. By contrast, when discounting is homogeneous, the MAC likelihood is invariant to group size.

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Bibliographic Info

Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP33.

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Length: pages
Date of creation: Oct 2002
Date of revision:
Handle: RePEc:roc:wallis:wp33

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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

Related research

Keywords: Repeated games; maximal average cooperation likelihood; heterogeneous discount factors; returns to scale;

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References

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  1. 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.
  2. 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.
  3. Matthew Haag & Roger Lagunoff, 2000. "social Norms, Local Interaction and Neighborhood Planning," Levine's Working Paper Archive 2049, David K. Levine.
  4. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
  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.
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Cited by:
  1. 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.
  2. Bowen, T. Renee & Zahran, Zaki, 2009. "On Dynamic Compromise," Research Papers 2020, Stanford University, Graduate School of Business.
  3. 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.
  4. Andrea Galeotti & Miguel Mel�ndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute.
  5. Andrea Galeotti & Miguel Mel�ndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute.
  6. Juan Escobar, 2008. "Cooperation and Self-Governance in Heterogeneous Communities," Discussion Papers 07-038, Stanford Institute for Economic Policy Research.
  7. Roger Lagunoff & Matthew Haag, 2002. "One Size and Structure of Group Cooperation," Working Papers gueconwpa~02-02-05, Georgetown University, Department of Economics.
  8. 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.
  9. 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.
  10. 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.

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