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Mistakes in cooperation: the stochastic stability of edgeworth's recontracting

  • Volij, Oscar
  • Serrano, Roberto

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 de Madrid. Departamento de Economía in its series UC3M Working papers. Economics 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. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. 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.
  3. 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.
  4. Volij, Oscar & Ben-Shoham, Asaf & Serrano, Roberto, 2004. "The Evolution of Exchange," Staff General Research Papers Archive 10247, Iowa State University, Department of Economics.
  5. Assaf Ben-Shoham & Roberto Serrano & Oscar Volig, 2000. "The Evolution of Change," Working Papers 2000-06, Brown University, Department of Economics.
  6. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
  7. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. 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.
  9. Nir Dagan & Roberto Serrano & Oscar Volij, 2000. "Bargaining, coalitions and competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 279-296, 03.
  10. 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.
  11. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2004. "Kidney Exchange," Scholarly Articles 2580565, Harvard University Department of Economics.
  12. 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.
  13. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  14. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  15. 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.
  16. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, March.
  17. 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.
  18. 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.
  19. Alejandro Manelli, 1989. "Monotonic Preferences and Core Equivalence," Discussion Papers 859, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. 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.
  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. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
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