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Rationalizability and mixed strategies in large games

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  • Jara-Moroni, Pedro

Abstract

We show that in large games with a finite set of actions in which the payoff of a player depends only on her own action and on an aggregate value that we call the (aggregate) state of the game, which is obtained from the complete action profile, it is possible to define and characterize the sets of (Point-)Rationalizable States in terms of pure and mixed strategies. We prove that the (Point-)Rationalizable States sets associated to pure strategies are equal to the sets of (Point-)Rationalizable States associated to mixed strategies. By example we show that, in general, the Point-Rationalizable States sets differ from the Rationalizable States sets.

Suggested Citation

  • Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    • Handle: RePEc:eee:ecolet:v:162:y:2018:i:c:p:153-156
    DOI: 10.1016/j.econlet.2017.11.023
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    References listed on IDEAS

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    1. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    2. Guesnerie, Roger, 1992. "An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis," American Economic Review, American Economic Association, vol. 82(5), pages 1254-1278, December.
    3. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
    4. Rath, Kali P., 1998. "Perfect and Proper Equilibria of Large Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 331-342, February.
    5. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
    6. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    7. Carmona, Guilherme, 2004. "On the purification of Nash equilibria of large games," Economics Letters, Elsevier, vol. 85(2), pages 215-219, November.
    8. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    9. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Rath, Kali P, 1995. "Representation of Finite Action Large Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 23-35.
    11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    12. Rath Kali P., 1994. "Some Refinements of Nash Equilibria of Large Games," Games and Economic Behavior, Elsevier, vol. 7(1), pages 92-103, July.
    13. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
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    More about this item

    Keywords

    Rationalizable strategies; Large games; Non-atomic games; Expectational coordination; Strong rationality;
    All these keywords.

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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