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Mistakes In Cooperation: The Stochastic Stability Of Edgeworth'S Recontracting

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Roberto Serrano ()
Oscar Volij ()

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Abstract

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake 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) non-singleton classes 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. The robustness of these results is confirmed in a weak coalitional recontracting process.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we056332.

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Date of creation: Nov 2005
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Handle: RePEc:cte:werepe:we056332

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  1. Michihiro Kandori & Roberto Serrano & Oscar Volij, 2004. "Decentralized Trade, Random Utility and the Evolution of Social Welfare," Economics Working Papers 0042, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  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. [Downloadable!] (restricted)
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  3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
  4. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July. [Downloadable!] (restricted)
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  5. Oscar Volij, 2000. "The Evolution of Exchange," Econometric Society World Congress 2000 Contributed Papers 0292, Econometric Society. [Downloadable!]
  6. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, Coalitions and Competition," Economics Working Papers 178, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  7. Roberto Serrano & Assaf Ben-Shoham & Oscar Volij, 2000. "The Evolution of Exchange," Economic theory and game theory 012, Oscar Volij. [Downloadable!]
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  8. 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.
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  9. Robert M. Anderson & William R. Zame, 1997. "Edgeworth's Conjecture with Infinitely Many Commodities: L1," Econometrica, Econometric Society, vol. 65(2), pages 225-274, March.
  10. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. [Downloadable!] (restricted)
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  11. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  12. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
  13. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May. [Downloadable!] (restricted)
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  14. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January. [Downloadable!] (restricted)
  15. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January. [Downloadable!] (restricted)
  16. Assaf Ben-Shoham & Roberto Serrano & Oscar Volig, 2000. "The Evolution of Change," Working Papers 2000-06, Brown University, Department of Economics.
  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  18. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1355-1384, December. [Downloadable!] (restricted)
  19. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, MIT Press, vol. 119(2), pages 457-488, May. [Downloadable!] (restricted)
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  20. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January. [Downloadable!] (restricted)
  21. 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. [Downloadable!] (restricted)
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  22. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457 Elsevier. [Downloadable!] (restricted)
  23. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August. [Downloadable!] (restricted)
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  1. Michihiro Kandori & Roberto Serrano & Oscar Volij, 2005. "Decentralized Trade, Random Utility And The Evolution Of Social Welfare," Economics Working Papers we056433, Universidad Carlos III, Departamento de Economía. [Downloadable!]
    Other versions:
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