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Information Spillover in Multiple Zero-sum Games

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  • Lucas Pahl

Abstract

This paper considers an infinitely repeated three-player Bayesian game with lack of information on two sides, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a generalization of the Aumann et al. [1] two-player zero-sum one-sided incomplete information model. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his long-term average payoffs. Our objective is to understand the adverse effects of \information spillover" from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects and characterize equilibrium payoffs. In a second result, we show how the effects of information spillover on the equilibrium payoff set of the informed player might be severe.

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  • Lucas Pahl, 2021. "Information Spillover in Multiple Zero-sum Games," Papers 2111.01647, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:2111.01647
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    References listed on IDEAS

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    1. Forges, Francoise, 1992. "Repeated games of incomplete information: Non-zero-sum," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 6, pages 155-177, Elsevier.
    2. repec:dau:papers:123456789/184 is not listed on IDEAS
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    4. Françoise Forges & Ulrich Horst & Antoine Salomon, 2016. "Feasibility and individual rationality in two-person Bayesian games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 11-36, March.
    5. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    6. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    7. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
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