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Compatible Beliefs and Equilibrium

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  • David Cass

    (Department of Economics, University of Pennsylvania)

Abstract

In this paper I investigate the nature of the beliefs which agents must hold (at least implicitly) in order to justify their considering various alternatives, in two distinct settings: the Walrasian model without production (with competitive equilibrium), and the sell-all version of the Shapley-Shubik market game (with Nash equilibrium). For this purpose I introduce a weak consistency requirement on behavior, one which I refer to as (having) compatible beliefs. My main conclusion is that, in this respect, these two versions of market allocation are essentially identical. For both, contemplating different choices requires varying the associated set of values of the variables defining compatible beliefs. And — though prima facie very different — it turns out that both equilibrium concepts can be recast entirely in terms of having compatible beliefs. My analysis also leads unequivocally to the interesting conclusion that, in the Walrasian model (even elaborated to encompass production, financial markets, and so on), budget constraints must hold, ab initio, with equality. This has one very important consequence: the First Basic Welfare Theorem, as usually stated, is false, as I demonstrate with two distinct counterexamples, the second of which is (in classical terms) unexceptional.

Suggested Citation

  • David Cass, 2006. "Compatible Beliefs and Equilibrium," PIER Working Paper Archive 06-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:06-009
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    References listed on IDEAS

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    1. Postlewaite, A & Schmeidler, David, 1978. "Approximate Efficiency of Non-Walrasian Nash Equilibria," Econometrica, Econometric Society, vol. 46(1), pages 127-135, January.
    2. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    5. Polemarchakis, H. M. & Siconolfi, P., 1993. "Competitive equilibria without free disposal or nonsatiation," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 85-99.
    6. Lionel W. McKenzie, 2005. "Classical General Equilibrium Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633302, December.
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    2. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, March.
    3. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.

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    JEL classification:

    • B49 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Other
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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