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On the Size and Structure of Group cooperation

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  • Matthew Haag
  • Roger Lagunoff

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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Suggested Citation

  • Matthew Haag & Roger Lagunoff, 2010. "On the Size and Structure of Group cooperation," Levine's Working Paper Archive 506439000000000043, David K. Levine.
  • Handle: RePEc:cla:levarc:506439000000000043
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    References listed on IDEAS

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    2. 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, February.
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    10. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142 World Scientific Publishing Co. Pte. Ltd..
    11. 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.
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    Citations

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    Cited by:

    1. Paul Pecorino, 2015. "Olson’s Logic of Collective Action at fifty," Public Choice, Springer, vol. 162(3), pages 243-262, March.
    2. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    3. Defever, Fabrice & Fischer, Christian & Suedekum, Jens, 2016. "Relational contracts and supplier turnover in the global economy," Journal of International Economics, Elsevier, vol. 103(C), pages 147-165.
    4. 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.
    5. 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.
    6. Elias Asproudis, 2011. "Revisiting environmental groups and members’ behaviour: budget, size and (im)pure altruism," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 13(2), pages 139-156, June.
    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. Juan Escobar, 2008. "Cooperation and Self-Governance in Heterogeneous Communities," Discussion Papers 07-038, Stanford Institute for Economic Policy Research.
    11. Bowen, T. Renee & Zahran, Zaki, 2012. "On dynamic compromise," Games and Economic Behavior, Elsevier, vol. 76(2), pages 391-419.
    12. Andrea Galeotti & Miguel Meléndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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