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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. 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.
  2. Volij, Oscar & Serrano, Roberto, 2000. "Bargaining, Coalitions and Competition," Staff General Research Papers 5107, Iowa State University, Department of Economics.
  3. Roberto Serrano & Assaf Ben-Shoham & Oscar Volij, 2000. "The Evolution of Exchange," Economic theory and game theory 012, Oscar Volij.
  4. 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.
  5. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. 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.
  7. 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.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. 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.
  10. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
  11. 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.
  12. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
  13. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
  14. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  15. 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.
  16. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2004. "Kidney Exchange," Scholarly Articles 2580565, Harvard University Department of Economics.
  17. 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.
  18. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January.
  19. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  20. Assaf Ben-Shoham & Roberto Serrano & Oscar Volig, 2000. "The Evolution of Change," Working Papers 2000-06, Brown University, Department of Economics.
  21. 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.
  22. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
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