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Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting

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  • Roberto Serrano
  • Oscar Volij

Abstract

We analyse a dynamic trading process of coalitional recontracting in an exchange economy with indivisible goods, where agents may make mistakes with small probability. According to this process, the resistance of a transition from one allocation to another is a function of the number of agents who make mistakes and of the seriousness of each mistake. If preferences are always strict, the unique stochastically stable state is the competitive equilibrium allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process. Copyright © The Author(s). Journal compilation © Royal Economic Society 2008.

Suggested Citation

  • Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
  • Handle: RePEc:ecj:econjl:v:118:y:2008:i:532:p:1719-1741
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    Cited by:

    1. Kandori, Michihiro & Serrano, Roberto & Volij, Oscar, 2008. "Decentralized trade, random utility and the evolution of social welfare," Journal of Economic Theory, Elsevier, vol. 140(1), pages 328-338, May.
    2. Kamijo, Yoshio & Kawasaki, Ryo, 2010. "Dynamics, stability, and foresight in the Shapley-Scarf housing market," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 214-222, March.
    3. Mandel, Antoine & Gintis, Herbert, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 84-92.
    4. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    5. Zhiwei Cui & Yan-An Hwang, 2017. "House exchange and residential segregation in networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 125-147, March.
    6. Newton, Jonathan & Wait, Andrew & Angus, Simon D., 2019. "Watercooler chat, organizational structure and corporate culture," Games and Economic Behavior, Elsevier, vol. 118(C), pages 354-365.
    7. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    8. Newton, Jonathan, 2015. "Stochastic stability on general state spaces," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 46-60.
    9. Tatur, Tymon, 2023. "Evolutionarily rational mutations in structured populations," Journal of Economic Theory, Elsevier, vol. 212(C).
    10. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.
    11. Mandel, Antoine & Gintis, Herbert, 2014. "Stochastic stability in the Scarf economy," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 44-49.
    12. Klaus, Bettina & Bochet, Olivier & Walzl, Markus, 2011. "A dynamic recontracting process for multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 84-98, January.
    13. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    14. Roland Pongou & Roberto Serrano, 2009. "A Dynamic Theory of Fidelity Networks with an Application to the Spread of HIV / AIDS," Working Papers wp2009_0909, CEMFI.
    15. Mandel Antoine & Botta Nicola, 2009. "A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-18, December.
    16. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    17. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    18. Kawasaki, Ryo, 2010. "Farsighted stability of the competitive allocations in an exchange economy with indivisible goods," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 46-52, January.
    19. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Farsighted house allocation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 817-824, September.
    20. Kawasaki, Ryo, 2015. "Roth–Postlewaite stability and von Neumann–Morgenstern stability," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 1-6.

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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