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Testable Restrictions of Nash Equilibrium in Games with Continuous Domains

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  • Andrés Carvajal

Abstract

This paper studies the falsifiability of the hypothesis of Nash behavior, for the case of a finite number of players who choose from continuous domains, subject to constraints. The results obtained here are negative. Assuming the observation of finite data sets, and using weak, but nontrivial, requirements for rationalizability, I show that the hypothesis is falsifiable, as it imposes nontautological, nonparametric testable restrictions. An assessment of these restrictions, however, shows that they are extremely weak, and that a researcher should expect, before observing the data set, that the test based on these restrictions will be passed by observed data. Without further specific assumptions, there do not exist harsher tests, since the conditions derived here also turn out to be sufficient. Moreover, ruling out the possibility that individuals may be cooperating so as to attain Pareto-efficient outcomes is impossible, as this behavior is in itself unfalsifiable with finite data sets. Imposing aggregation, or strategic complementarity and/or substitutability, if theoretically plausible, may provide for a harsher test.

Suggested Citation

  • Andrés Carvajal, 2003. "Testable Restrictions of Nash Equilibrium in Games with Continuous Domains," Borradores de Economia 3555, Banco de la Republica.
    • Handle: RePEc:col:000094:003555
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    References listed on IDEAS

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    1. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
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    7. Donald J. Brown & Rosa L. Matzkin, 2008. "Testable Restrictions on the Equilibrium Manifold," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 11-25, Springer.
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    Cited by:

    1. Andrés Carvajal, 2003. "Testable Restrictions og General Equilibrium Theory in Exchange Economies with Externalities," Borradores de Economia 3556, Banco de la Republica.
    2. Carvajal, Andres & Quah, John K.-H., 2009. "A Nonparametric Analysis of the Cournot Model," The Warwick Economics Research Paper Series (TWERPS) 922, University of Warwick, Department of Economics.
    3. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 349-378, October.

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    Keywords

    Game theory;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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