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Compromise, Don't Optimize: Generalizing Perfect Bayesian Equilibrium to Allow for Ambiguity

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  • Karl Schlag
  • Andriy Zapechelnyuk

Abstract

We introduce a solution concept for extensive-form games of incomplete information in which players need not assign likelihoods to what they do not know about the game. This is embedded in a model in which players can hold multiple priors. Players make choices by looking for compromises that yield a good performance under each of their updated priors. Our solution concept is called perfect compromise equilibrium. It generalizes perfect Bayesian equilibrium. We show how it deals with ambiguity in Cournot and Bertrand markets, public good provision, Spence's job market signaling, bilateral trade with common value, and forecasting.

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  • Karl Schlag & Andriy Zapechelnyuk, 2020. "Compromise, Don't Optimize: Generalizing Perfect Bayesian Equilibrium to Allow for Ambiguity," Papers 2003.02539, arXiv.org, revised Sep 2021.
    • Handle: RePEc:arx:papers:2003.02539
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    References listed on IDEAS

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    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    2. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    3. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
    4. Subir K. Chakrabarti & Iryna Topolyan, 2016. "An extensive form-based proof of the existence of sequential equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 355-365, October.
    5. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    6. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
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