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

Author

Listed:
  • Roberto Serrano

    () (Department of Economics, Brown University)

  • Oscar Volij

    () (Department of Economics, Iowa State University)

Abstract

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents may make mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake free) process consist of (i) all core allocations as absorbing states, and (ii) cycles of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes-–do not improve–-in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not.

Suggested Citation

  • Roberto Serrano & Oscar Volij, 2003. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economics Working Papers 0029, Institute for Advanced Study, School of Social Science.
  • Handle: RePEc:ads:wpaper:0029
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    References listed on IDEAS

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    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. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
    3. Roberto Serrano & Rajiv Vohra & Oscar Volij, 2001. "On the Failure of Core Convergence in Economies with Asymmetric Information," Econometrica, Econometric Society, vol. 69(6), pages 1685-1696, November.
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    Cited by:

    1. 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.
    2. Mandel, Antoine & Gintis, Herbert, 2014. "Stochastic stability in the Scarf economy," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 44-49.
    3. repec:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-015-0526-2 is not listed on IDEAS
    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. 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.
    6. 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.
    7. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    8. 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.
    9. 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.
    10. 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.
    11. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Farsighted house allocation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 817-824, September.
    12. Newton, Jonathan & Wait, Andrew & Angus, Simon D., 2016. "Watercooler chat, organizational structure and corporate culture," Working Papers 2016-03, University of Sydney, School of Economics.
    13. Kawasaki, Ryo, 2015. "Roth–Postlewaite stability and von Neumann–Morgenstern stability," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 1-6.
    14. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    15. 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.
    16. 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.
    17. Newton, Jonathan, 2015. "Stochastic stability on general state spaces," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 46-60.
    18. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.

    More about this item

    Keywords

    Stochastic Stability; Exchange Economies; Assignment Problems; Core; Walrasian Equilibrium;

    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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