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On the Size and Structure of Group Cooperation

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  • Matthew Haag

    (University of Warwick)

  • Roger Lagunoff

    (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 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.

Suggested Citation

  • Matthew Haag & Roger Lagunoff, 2002. "On the Size and Structure of Group Cooperation," Game Theory and Information 0209005, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0209005
    Note: Type of Document - pdf; prepared on PC; to print on postscript; pages: 31 ; figures: included ;
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    References listed on IDEAS

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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. Wang, Xiaofeng & Chen, Xiaojie & Gao, Jia & Wang, Long, 2013. "Reputation-based mutual selection rule promotes cooperation in spatial threshold public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 181-187.
    4. 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.
    5. 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.
    6. Guillaume Cheikbossian, 2019. "Group cooperation against an incumbent," Working Papers hal-02378829, HAL.
    7. 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.
    8. 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.
    9. Ani Dasgupta & Sambuddha Ghosh, 2017. "Repeated Games Without Public Randomization: A Constructive Approach," Boston University - Department of Economics - Working Papers Series WP2017-011, Boston University - Department of Economics, revised Feb 2019.
    10. Polanski, Arnold, 2024. "Close-knit neighborhoods: Stability of cooperation in networks," Journal of Economic Theory, Elsevier, vol. 215(C).
    11. 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.
    12. Bowen, T. Renee & Zahran, Zaki, 2012. "On dynamic compromise," Games and Economic Behavior, Elsevier, vol. 76(2), pages 391-419.
    13. 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.
    14. Zeng, Weijun & Ai, Hongfeng & Zhao, Man, 2019. "Asymmetrical expectations of future interaction and cooperation in the iterated prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 148-164.
    15. 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.
    16. Banaszak, Ilona, 2009. "Determinanty Sukcesu Współpracy Na Rynkach Rolniczych Na Przykładzie Grup Producentów Rolnych W Polsce," Village and Agriculture (Wieś i Rolnictwo), Polish Academy of Sciences (IRWiR PAN), Institute of Rural and Agricultural Development, vol. 1(142).
    17. Balmaceda, Felipe & Escobar, Juan F., 2017. "Trust in cohesive communities," Journal of Economic Theory, Elsevier, vol. 170(C), pages 289-318.
    18. Guillaume Cheikbossian, 2021. "Group cooperation against a hegemon," Journal of Theoretical Politics, , vol. 33(1), pages 25-55, January.
    19. Juan Escobar, 2008. "Cooperation and Self-Governance in Heterogeneous Communities," Discussion Papers 07-038, Stanford Institute for Economic Policy Research.
    20. Andrea Galeotti & Miguel Meléndez, 2004. "Exploitation and Cooperation in Networks," Tinbergen Institute Discussion Papers 04-076/1, Tinbergen Institute.
    21. Dasgupta, Ani & Ghosh, Sambuddha, 2022. "Self-accessibility and repeated games with asymmetric discounting," Journal of Economic Theory, Elsevier, vol. 200(C).

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    More about this item

    Keywords

    Repeated games; maximal average cooperation likelihood; heterogeneous discount factors; returns to scale;
    All these keywords.

    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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