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

  • Roberto Serrano

    ()

  • Oscar Volij

    ()

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," Working Papers 2004-06, Brown University, Department of Economics.
  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. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  4. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  5. Ben-Shoham, Assaf & Serrano, Roberto & Volij, Oscar, 2004. "The evolution of exchange," Journal of Economic Theory, Elsevier, vol. 114(2), pages 310-328, February.
  6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  7. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
  8. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," Game Theory and Information 0308002, EconWPA.
  9. 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.
  10. 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.
  11. 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.
  12. Hideo Konishi & Debraj Ray, 2000. "Coalition Formation as a Dynamic Process," Boston College Working Papers in Economics 478, Boston College Department of Economics, revised 15 Apr 2002.
  13. Roberto Serrano & Rajiv Vohra & Oscar Volij, 1999. "On the Failure of Core Convergence in Economies with Asymmetric Information," Working Papers 99-22, Brown University, Department of Economics.
  14. Assaf Ben-Shoham & Roberto Serrano & Oscar Volig, 2000. "The Evolution of Change," Working Papers 2000-06, Brown University, Department of Economics.
  15. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
  16. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, Coalitions, and Competition," Economic theory and game theory 014, Nir Dagan, revised May 1999.
  17. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  18. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January.
  19. Gomes, Armando R & Jehiel, Philippe, 2001. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," CEPR Discussion Papers 3012, C.E.P.R. Discussion Papers.
  20. 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.
  21. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
  22. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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