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Stochastic stability in the Scarf economy

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  • Antoine Mandel

    ()
    (Centre d'Economie de la Sorbonne)

  • Herbert Gintis

    ()
    (Santa Fe Institute and Central European University)

Abstract

We present a mathematical model for the analysis of the bargaining games based on private prices used by Gintis to simulate the dynamics of prices in exchange economies, see [Gintis 2007]. We then characterize, in the Scarf economy, a class of dynamics for which the Walrasian equilibrium is the only stochastically stable state. Hence, we provide dynamic foundations for general equilibrium for one of the best-known example of instability of the tâtonement process.

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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12066.

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Length: 14 pages
Date of creation: Oct 2012
Date of revision:
Handle: RePEc:mse:cesdoc:12066

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  1. Schecter, Stephen, 1977. "Accessibility of optima in pure exchange economies," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 197-216, December.
  2. Herbert Gintis, 2007. "The Dynamics of General Equilibrium," Economic Journal, Royal Economic Society, vol. 117(523), pages 1280-1309, October.
  3. Alok Kumar & Martin Shubik, 2001. "Variations on the Theme of Scarf's Counter-Example," Working Papers 01-12-074, Santa Fe Institute.
  4. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  7. Scarf, Herbert, 1981. "Comment on: "On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example"," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 469-70, June.
  8. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  9. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  10. Roberto Serrano & Oscar Volij, 2005. "Mistakes In Cooperation: The Stochastic Stability Of Edgeworth'S Recontracting," Economics Working Papers we056332, Universidad Carlos III, Departamento de Economía.
  11. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
  12. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
  13. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  14. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  15. Ghosal, Sayantan & Porter, James, 2013. "Decentralised exchange, out-of-equilibrium dynamics and convergence to efficiency," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 1-21.
  16. repec:hal:cesptp:halshs-00634656 is not listed on IDEAS
  17. Arkit, Aleksandra, 2003. "Globally stable price dynamics," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 27-38, February.
  18. Herings, P.J.J., 1994. "A globally and universally stable price adjustment process," Discussion Paper 1994-52, Tilburg University, Center for Economic Research.
  19. Mandel Antoine & Botta Nicola, 2009. "A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-18, December.
  20. Scarf, Herbert, 1969. "An Example of an Algorithm for Calculating General Equilibrium Prices," American Economic Review, American Economic Association, vol. 59(4), pages 669-77, Part I Se.
  21. Steven Tucker & Charles Noussair & Sean Crockett, 2013. "Price Dynamics In General Equilibrium Experiments," Journal of Economic Surveys, Wiley Blackwell, vol. 27(3), pages 421-438, 07.
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