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Stochastic stability in the Scarf economy

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  • Antoine Mandel

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Herbert Gintis

    (Santa Fe Institute - Santa Fe Institute, Central European University - CEU - 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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00748328.

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Date of creation: Oct 2012
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Handle: RePEc:hal:cesptp:halshs-00748328

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Keywords: General Equilibrium; exchange economies; bargaining games; stochastic stability.;

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  1. Herings, P.J.J., 1994. "A globally and universally stable price adjustment process," Discussion Paper, Tilburg University, Center for Economic Research 1994-52, Tilburg University, Center for Economic Research.
  2. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 469-70, June.
  3. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
  4. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Steven Tucker & Charles Noussair & Sean Crockett, 2013. "Price Dynamics In General Equilibrium Experiments," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 27(3), pages 421-438, 07.
  6. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
  9. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  10. Arkit, Aleksandra, 2003. "Globally stable price dynamics," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 27-38, February.
  11. Roberto Serrano & Oscar Volij, 2003. "MISTAKE IN COOPERATION:the Stochastic Stability of Edgeworth's Recontracting," Working Papers, Brown University, Department of Economics 2003-23, Brown University, Department of Economics.
  12. Alok Kumar & Martin Shubik, 2001. "Variations on the Theme of Scarf's Counter-Example," Working Papers, Santa Fe Institute 01-12-074, Santa Fe Institute.
  13. 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), HAL halshs-00634656, HAL.
  14. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, Elsevier, vol. 6(4), pages 345-354, August.
  15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  16. Ghosal, Sayantan & Porter, James, 2013. "Decentralised exchange, out-of-equilibrium dynamics and convergence to efficiency," Mathematical Social Sciences, Elsevier, Elsevier, vol. 66(1), pages 1-21.
  17. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 43(3), pages 513-18, May.
  18. Scarf, Herbert, 1969. "An Example of an Algorithm for Calculating General Equilibrium Prices," American Economic Review, American Economic Association, American Economic Association, vol. 59(4), pages 669-77, Part I Se.
  19. Schecter, Stephen, 1977. "Accessibility of optima in pure exchange economies," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 197-216, December.
  20. Herbert Gintis, 2007. "The Dynamics of General Equilibrium," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 117(523), pages 1280-1309, October.
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