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A Multi-Stage Market Game that Implements any Walrasian Allocation in any Pure-Exchange Environment

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  • Mouhua Liao

Abstract

This paper studies retrading in a multi-stage Shapley--Shubik structure market game with symmetric limit orders and a finite number of agents. Without restrictions on preferences and endowments, a constructive proof is used to show that any Walrasian allocation can be implemented by a Markov perfect equilibrium if agents are allowed to retrade for a finite number of rounds before they consume. As part of the proof, we give a closed form expression for the required number of rounds, which depends on the Walrasian allocation and the selection of a numeraire.

Suggested Citation

  • Mouhua Liao, 2019. "A Multi-Stage Market Game that Implements any Walrasian Allocation in any Pure-Exchange Environment," Working Papers 2019-07-03, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    • Handle: RePEc:wyi:wpaper:002432
    as

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    References listed on IDEAS

    as
    1. Dubey, Pradeep & Geanakoplos, John, 2003. "From Nash to Walras via Shapley-Shubik," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 391-400, July.
    2. Ghosal, Sayantan & Morelli, Massimo, 2004. "Retrading in market games," Journal of Economic Theory, Elsevier, vol. 115(1), pages 151-181, March.
    3. Dubey, Pradeep, 1982. "Price-Quantity Strategic Market Games," Econometrica, Econometric Society, vol. 50(1), pages 111-126, January.
    4. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    5. Dubey, Pradeep & Sahi, Siddharta & Shubik, Martin, 1993. "Repeated trade and the velocity of money," Journal of Mathematical Economics, Elsevier, vol. 22(2), pages 125-137.
    6. Aumann, Robert J., 1976. "An elementary proof that integration preserves uppersemicontinuity," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 15-18, March.
    7. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    8. Liao, Mouhua, 2016. "A market game with symmetric limit orders," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 66-76.
    9. Leo K. Simon, 1984. "Bertrand, the Cournot Paradigm and the Theory of Perfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(2), pages 209-230.
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    More about this item

    Keywords

    Market game; Retrading; Symmetric limit orders; Walrasian equilibrium.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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