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On the existence of pure-strategy equilibria in games with private information: A complete characterization

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  • Khan, M. Ali
  • Zhang, Yongchao

Abstract

This paper reports a definitive resolution to the question of the existence of a pure-strategy Bayesian–Nash equilibrium in games with a finite number of players, each with a compact metric action set and private information. The resolution hinges on saturated spaces. If the individual spaces of information are saturated, there exists a pure-strategy equilibrium in such a game; and if there exists a pure-strategy equilibrium for the class of games under consideration and with uncountable action sets, the spaces of private information must be saturated. As such, the paper offers a complete characterization of a longstanding question, and offers another game-theoretic characterization of the saturation property, one that complements a recent result of Keisler–Sun (2009) on large non-anonymous games with complete information.

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  • Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 197-202.
    • Handle: RePEc:eee:mateco:v:50:y:2014:i:c:p:197-202
    DOI: 10.1016/j.jmateco.2013.12.005
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    Cited by:

    1. Beißner, Patrick & Khan, M. Ali, 2019. "On Hurwicz–Nash equilibria of non-Bayesian games under incomplete information," Games and Economic Behavior, Elsevier, vol. 115(C), pages 470-490.
    2. Yuhki Hosoya & Chaowen Yu, 2021. "On the Approximate Purification of Mixed Strategies in Games with Infinite Action Sets," Papers 2103.07736, arXiv.org, revised Apr 2022.
    3. Chaowen Yu & Yuhki Hosoya & Toru Maruyama, 2018. "On the purification of mixed strategies," Economics Bulletin, AccessEcon, vol. 38(3), pages 1655-1675.
    4. Einy, Ezra & Haimanko, Ori, 2020. "Equilibrium existence in games with a concave Bayesian potential," Games and Economic Behavior, Elsevier, vol. 123(C), pages 288-294.
    5. Zeng, Yishu, 2023. "Derandomization of persuasion mechanisms," Journal of Economic Theory, Elsevier, vol. 212(C).
    6. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
    7. M. Ali Khan & Yongchao Zhang, 2017. "Existence of pure-strategy equilibria in Bayesian games: a sharpened necessity result," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 167-183, March.
    8. Fu, Haifeng & Yu, Haomiao, 2018. "Pareto refinements of pure-strategy equilibria in games with public and private information," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 18-26.
    9. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    10. Yuhki Hosoya & Chaowen Yu, 2022. "On the approximate purification of mixed strategies in games with infinite action sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 69-93, May.
    11. Khan, M. Ali & Zhang, Yongchao, 2018. "On pure-strategy equilibria in games with correlated information," Games and Economic Behavior, Elsevier, vol. 111(C), pages 289-304.

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