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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 falsiability of the hypothesis of Nash behavoir, 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 non-trivial, requirements for rationalizability, I show that the hypotesis 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 specif 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 complementary and/or substitutability, if theoretically plausible, may provide for a harsher test.

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Paper provided by Banco de la Republica de Colombia in its series Borradores de Economia with number 229.

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Handle: RePEc:bdr:borrec:229

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Keywords: Game theory; testable restrictions; revealed preferences.;

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  1. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers 00/15, Department of Economics, University of York.
  2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  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. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  5. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
  6. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  7. Varian, Hal R, 1983. "Non-Parametric Tests of Consumer Behaviour," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 99-110, January.
  8. 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.
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Cited by:
  1. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer, vol. 45(1), pages 349-378, October.
  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, 2003. "Testable Restrictions og General Equilibrium Theory in Exchange Economies with Externalities," BORRADORES DE ECONOMIA 003556, BANCO DE LA REPÚBLICA.

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