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From Nash to Walras via Shapley-Shubik

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Abstract

We derive the existence of a Walras equilibrium directly from Nash's theorem on noncooperative games. No price player is involved, nor are generalized games. Instead we use a variant of the Shapley-Shubik trading-post game.

Suggested Citation

  • Pradeep Dubey & John Geanakoplos, 2002. "From Nash to Walras via Shapley-Shubik," Cowles Foundation Discussion Papers 1360, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1360
    Note: CFP 1065.
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d13/d1360.pdf
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    References listed on IDEAS

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    1. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 217-225.
    2. Amir, Rabah & Sahi, Siddharta & Shubik, Martin & Yao, Shuntian, 1990. "A strategic market game with complete markets," Journal of Economic Theory, Elsevier, vol. 51(1), pages 126-143, June.
    3. Sorin, Sylvain, 1996. "Strategic Market Games with Exchange Rates," Journal of Economic Theory, Elsevier, vol. 69(2), pages 431-446, May.
    4. Postlewaite, A & Schmeidler, David, 1978. "Approximate Efficiency of Non-Walrasian Nash Equilibria," Econometrica, Econometric Society, vol. 46(1), pages 127-135, January.
    5. Florig, Michael, 2001. "Hierarchic competitive equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(4), pages 515-546, July.
    6. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    7. Dubey, Pradeep, 1982. "Price-Quantity Strategic Market Games," Econometrica, Econometric Society, vol. 50(1), pages 111-126, January.
    8. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-1593, November.
    9. 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.
    10. Gerard Debreu, 1961. "New Concepts and Techniques for Equilibrium Analysis," Cowles Foundation Discussion Papers 129, Cowles Foundation for Research in Economics, Yale University.
    11. Jaynes, Gerald David & Okuno, Masahiro & Schmeidler, David, 1978. "Efficiency in an Atomless Economy with Fiat Money," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(1), pages 149-156, February.
    12. Danilov, V. I. & Sotskov, A. I., 1990. "A generalized economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 19(4), pages 341-356.
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    Citations

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    Cited by:

    1. Manfred Nermuth, 2008. "The Structure of Equilibrium in an Asset Market with Variable Supply," Vienna Economics Papers 0804, University of Vienna, Department of Economics.
    2. Hervés-Beloso, Carlos & Moreno-García, Emma, 2009. "Walrasian analysis via two-player games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 220-233, January.
    3. Faias, Marta & Moreno, Emma & Wooders, Myrna, 2009. "A Strategic market game approach for the private provision of public goods," MPRA Paper 37777, University Library of Munich, Germany, revised 08 Mar 2012.
    4. Hens, Thorsten & Reimann, Stefan & Vogt, Bodo, 2004. "Nash competitive equilibria and two-period fund separation," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 321-346, June.
    5. Ehud Kalai, 2006. "Structural Robustness of Large Games," Discussion Papers 1431, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. repec:spr:joecth:v:66:y:2018:i:2:d:10.1007_s00199-017-1068-6 is not listed on IDEAS
    7. Guadalupe Fugarolas-Alvarez-Ude & Carlos Hervés-Beloso & Emma Moreno-García & Juan Torres-Martínez, 2009. "A market game approach to differential information economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 321-330, February.
    8. Peter J. Hammond, 2017. "Designing a strategyproof spot market mechanism with many traders: twenty-two steps to Walrasian equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 1-50, January.
    9. Faias, Marta & Hervés-Beloso, Carlos & Moreno García, Emma, 2009. "A price mechanism in economies with asymmetric information," MPRA Paper 15176, University Library of Munich, Germany.
    10. Pradeep Dubey & Siddhartha Sahi & Martin Shubik, 2014. "Minimally complex exchange mechanisms: Emergence of prices, markets, and money," Department of Economics Working Papers 14-01, Stony Brook University, Department of Economics.
    11. Fugarolas, Guadalupe, 2006. "Nash equilibria applied to Spot-financial equilibria in General equilibrium incomplete market models," MPRA Paper 470, University Library of Munich, Germany.
    12. Liao, Mouhua, 2016. "A market game with symmetric limit orders," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 66-76.
    13. repec:eee:mateco:v:72:y:2017:i:c:p:95-103 is not listed on IDEAS
    14. Dmitry Levando, 2012. "A Survey Of Strategic Market Games," Economic Annals, Faculty of Economics, University of Belgrade, vol. 57(194), pages 63-106, July - Se.
    15. repec:eee:gamebe:v:108:y:2018:i:c:p:452-465 is not listed on IDEAS

    More about this item

    Keywords

    Nash equilibrium; Walras equilibrium; Shapley-Shubik trading-posts game; Money;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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