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Testable Restrictions of Nash Equilibrium in Games with Continuous Domains

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  • Andrés Carvajal

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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.

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Bibliographic Info

Paper provided by BANCO DE LA REPÚBLICA in its series BORRADORES DE ECONOMIA with number 003555.

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Length: 54
Date of creation: 31 Jan 2003
Date of revision:
Handle: RePEc:col:000094:003555

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Keywords: Game theory;

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  1. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
  2. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  3. Donald J. Brown & Rosa L. Matzkin, 1995. "Testable Restrictions on the Equilibrium Manifold," Cowles Foundation Discussion Papers 1109, Cowles Foundation for Research in Economics, Yale University.
  4. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-91, May.
  5. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers 00/15, Department of Economics, University of York.
  6. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  8. Varian, Hal R, 1983. "Non-Parametric Tests of Consumer Behaviour," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 99-110, January.
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Cited by:
  1. Andrés Carvajal, 2004. "Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities," Royal Holloway, University of London: Discussion Papers in Economics 04/28, Department of Economics, Royal Holloway University of London, revised Nov 2004.
  2. Andrés Carvajal & John Quah, 2009. "A Nonparametric Analysis of the Cournot Model," Economics Papers 2009-W15, Economics Group, Nuffield College, University of Oxford.
  3. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer, vol. 45(1), pages 349-378, October.

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