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Dynamic group formation in the repeated prisonerʼs dilemma

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  • Maruta, Toshimasa
  • Okada, Akira

Abstract

We consider dynamic group formation in repeated n-person prisonerʼs dilemma. Agreements in coalitional bargaining are self-binding in that they are supported as subgame perfect equilibria of repeated games. Individuals are allowed to renegotiate the cooperating group agreement through a process of voluntary participation. We prove that a cooperating group forms as an absorbing state of a Markov perfect equilibrium after a finite number of renegotiations if and only if the group is Pareto efficient, provided that individuals are patient. The cooperating group can only expand.

Suggested Citation

  • Maruta, Toshimasa & Okada, Akira, 2012. "Dynamic group formation in the repeated prisonerʼs dilemma," Games and Economic Behavior, Elsevier, vol. 74(1), pages 269-284.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:269-284
    DOI: 10.1016/j.geb.2011.05.006
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    1. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
    2. Armando Gomes & Philippe Jehiel, 2005. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 626-667, June.
    3. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    4. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    5. Michael Kosfeld & Akira Okada & Arno Riedl, 2009. "Institution Formation in Public Goods Games," American Economic Review, American Economic Association, vol. 99(4), pages 1335-1355, September.
    6. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    7. Furusawa, Taiji & Lai, Edwin L. -C., 1999. "Adjustment costs and gradual trade liberalization," Journal of International Economics, Elsevier, vol. 49(2), pages 333-361, December.
    8. Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(2), pages 339-356.
    9. Bloch, Francis & Gomes, Armando, 2006. "Contracting with externalities and outside options," Journal of Economic Theory, Elsevier, vol. 127(1), pages 172-201, March.
    10. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    11. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    12. Akira Okada, 2000. "The Efficiency Principle in Non-Cooperative Coalitional Bargaining," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 34-50, March.
    13. Dixit, Avinash & Olson, Mancur, 2000. "Does voluntary participation undermine the Coase Theorem?," Journal of Public Economics, Elsevier, vol. 76(3), pages 309-335, June.
    14. Kyle Hyndman & Debraj Ray, 2007. "Coalition Formation with Binding Agreements," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1125-1147.
    15. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, vol. 73(4), pages 1329-1350, July.
    16. Daniel J. Seidmann & Eyal Winter, 1998. "A Theory of Gradual Coalition Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(4), pages 793-815.
    17. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    18. Kalyan Chatterjee & Hamid Sabourian, 2000. "Multiperson Bargaining and Strategic Complexity," Econometrica, Econometric Society, vol. 68(6), pages 1491-1510, November.
    19. Watson, Joel, 1999. "Starting Small and Renegotiation," Journal of Economic Theory, Elsevier, vol. 85(1), pages 52-90, March.
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    Cited by:

    1. OKADA, Akira & 岡田, 章, 2014. "International Cooperation and Institution Formation: A Game Theoretic Perspective," Discussion Papers 2014-17, Graduate School of Economics, Hitotsubashi University.
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    4. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    5. Akira Okada, 2018. "Non-cooperative Bargaining for Side Payments Contract," KIER Working Papers 983, Kyoto University, Institute of Economic Research.

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    More about this item

    Keywords

    Group formation; Prisonerʼs dilemma; Repeated games; Non-cooperative coalitional bargaining; Efficiency; Renegotiation;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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