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Testable Restrictions of Nash Equilibrium in Games with Continuous Domains

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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 Department of Economics, Royal Holloway University of London in its series Royal Holloway, University of London: Discussion Papers in Economics with number 04/26.

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Length: 57 pages
Date of creation: Nov 2004
Date of revision: Nov 2004
Handle: RePEc:hol:holodi:0426

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Keywords: Game theory; testable restrictions; revealed preferences;

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  1. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  2. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers 00/15, Department of Economics, University of York.
  3. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
  4. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  5. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  6. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  7. 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.
  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, . "Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities," Borradores de Economia 231, Banco de la Republica de Colombia.
  2. John Quah & Andres Carvajal, 2009. "A Nonparametric Analysis of the Cournot Model," Economics Series Working Papers 465, University of Oxford, Department of Economics.
  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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