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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)

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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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Publisher 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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Date of creation: Oct 2002
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Handle: RePEc:roc:wallis:wp33

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Postal: UNIVERSITY OF ROCHESTER, Wallis Institute, HARKNESS 109B ROCHESTER NEW YORK 14627 U.S.A.

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

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D62 - Microeconomics - - Welfare Economics - - - Externalities
D7 - Microeconomics - - Analysis of Collective Decision-Making

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107 Elsevier. [Downloadable!] (restricted)
  3. Haag, Matthew & Lagunoff, Roger, 2002. "On the Size and Structure of Group Cooperation," The Warwick Economics Research Paper Series (TWERPS) 650, University of Warwick, Department of Economics. [Downloadable!]
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  4. Esteban, J. & Ray, D., 1999. "Collective Action and Group Size Paradox," Papers 23, El Instituto de Estudios Economicos de Galicia Pedro Barrie de la Maza.
  5. Mailath, George J & Postlewaite, Andrew, 1990. "Asymmetric Information Bargaining Problems with Many Agents," Review of Economic Studies, Blackwell Publishing, vol. 57(3), pages 351-67, July. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  7. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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  9. 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.
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  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. [Downloadable!] (restricted)
  11. Fudenberg, Drew & Kreps, David M & Maskin, Eric S, 1990. "Repeated Games with Long-run and Short-run Players," Review of Economic Studies, Blackwell Publishing, vol. 57(4), pages 555-73, October. [Downloadable!] (restricted)
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  12. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
  13. 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. [Downloadable!] (restricted)
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  14. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Haag, Matthew & Lagunoff, Roger, 2007. "On the size and structure of group cooperation," Journal of Economic Theory, Elsevier, vol. 135(1), pages 68-89, July. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!] (restricted)
  3. Andrea Galeotti & Miguel Meléndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute. [Downloadable!]
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