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Rationalizability in games with a continuum of players

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  • Jara-Moroni, Pedro
Abstract
The concept of rationalizability has been used in the last fifteen years to study stability of equilibria in models with a continuum of agents such as competitive markets, macroeconomic dynamics and currency attacks. However, rationalizability has been formally defined in general settings only for games with a finite number of players. We propose an exploration of rationalizability in the context of games with a continuum of players. We deal with a special class of these games, in which payoff of each player depends only on his own strategy and on an aggregate value: the state of the game, which is obtained from the complete action profile. We define the sets of point-rationalizable states and rationalizable states. For the case of continuous payoffs and compact strategy sets, we characterize these sets and prove their convexity and compactness. We provide as well results on the equivalence of point- and standard-rationalizability.

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  • Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    • Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:668-684
    DOI: 10.1016/j.geb.2012.03.004
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    Cited by:

    1. Roger Guesnerie & Pedro Jara-Moroni, 2011. "Expectational coordination in simple economic contexts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 205-246, June.
    2. Roger Guesnerie & Pedro Jara-Moroni, 2009. "Expectational coordination in simple economic contexts: concepts and analysis with emphasis on strategic substitutabilities," PSE Working Papers halshs-00574957, HAL.
    3. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Schmeidler, David, 2022. "Equilibria of nonatomic anonymous games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 110-131.
    4. Hector Calvo-Pardo, 2009. "Are the antiglobalists right? Gains-from-trade without a Walrasian auctioneer," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(3), pages 561-592, March.
    5. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    6. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    7. Khan, Mohammed Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2017. "On the equivalence of large individualized and distributionalized games," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    9. Qiao, Lei & Yu, Haomiao, 2014. "On the space of players in idealized limit games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 177-190.
    10. Qiao, Lei & Yu, Haomiao & Zhang, Zhixiang, 2016. "On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization," Games and Economic Behavior, Elsevier, vol. 99(C), pages 89-98.
    11. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.

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    More about this item

    Keywords

    Rationalizable strategies; Non-atomic games; Expectational coordination; Rational expectations; Eductive stability; 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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