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

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  • Roberto Serrano

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  • Oscar Volij

    ()

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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Bibliographic Info

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. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January.
  2. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  3. 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.
  4. 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.
  5. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," NBER Working Papers 10002, National Bureau of Economic Research, Inc.
  6. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Armo Gomes & Philippe Jehiel, 2001. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," Penn CARESS Working Papers 76ff153ae29996d16c454e473, Penn Economics Department.
  8. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, 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. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
  11. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July.
  12. Roberto Serrano & Assaf Ben-Shoham & Oscar Volij, 2000. "The Evolution of Exchange," Economic theory and game theory 012, Oscar Volij.
  13. Perry, M. & Rany, P., 1992. "A Non-Cooperative View of Coalition Formation and the Core," UWO Department of Economics Working Papers 9203, University of Western Ontario, Department of Economics.
  14. Roberto Serrano & Rajiv Vohra & Oscar Volij, 2000. "On the Failure of Core Convergence in Economies with Asymmetric Information," Econometric Society World Congress 2000 Contributed Papers 0141, Econometric Society.
  15. 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.
  16. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, Coalitions, and Competition," Economic theory and game theory 014, Nir Dagan, revised May 1999.
  17. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  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.
  19. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  20. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
  21. Assaf Ben-Shoham & Roberto Serrano & Oscar Volig, 2000. "The Evolution of Change," Working Papers 2000-06, Brown University, Department of Economics.
  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.
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Cited by:
  1. Michihiro Kandori & Roberto Serrano & Oscar Volij, 2004. "Decentralized Trade, Random Utility and the Evolution of Social Welfare," CIRJE F-Series CIRJE-F-286, CIRJE, Faculty of Economics, University of Tokyo.
  2. Antoine Mandel & Herbert Gintis, 2012. "Stochastic stability in the Scarf economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00748328, HAL.
  3. Roberto Serrano & Roland Pongou, 2009. "A Dynamic Theory Of Fidelity Networks With An Application To The Spread Of Hiv/Aids," Working Papers wp2009_0909, CEMFI.
  4. Antoine Mandel & Nicola Botta, 2009. "A note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00634656, HAL.
  5. Bettina-Elisabeth Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted House Allocation," Harvard Business School Working Papers 09-129, Harvard Business School.
  6. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
  7. Bettina Klaus & Flip Klijn & Markus Walzl, 2008. "Stochastic Stability for Roommate Markets," Working Papers 357, Barcelona Graduate School of Economics.

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