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Payoff Continuity in Games of Incomplete Information Across Models of Knowledge

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  • Ashwin Kambhampati

Abstract

Equilibrium predictions in games of incomplete information are sensitive to the assumed information structure. Monderer and Samet (1996) and Kajii and Morris (1998) define topological notions of proximity for common prior information structures such that two information structures are close if and only if (approximate) equilibrium payoffs are close. However, Monderer and Samet (1996) fix a common prior and define their topology on profiles of partitions over a state space, whereas Kajii and Morris (1998) define their topology on common priors over the product of a state space and a type space. We prove the open conjecture that two partition profiles are close in the Monderer and Samet (1996) topology if and only if there exists a labeling of types such that the associated common priors are close in the Kajii and Morris (1998) topology.

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  • Ashwin Kambhampati, 2025. "Payoff Continuity in Games of Incomplete Information Across Models of Knowledge," Papers 2512.03982, arXiv.org.
    • Handle: RePEc:arx:papers:2512.03982
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    References listed on IDEAS

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    1. Dov Monderer & Dov Samet, 1996. "Proximity of Information in Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 707-725, August.
    2. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
    3. Gensbittel, Fabien & Pęski, Marcin & Renault, Jérôme, 2022. "Value-based distance between information structures," Theoretical Economics, Econometric Society, vol. 17(3), July.
    4. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    5. Rothschild, Casey G., 2005. "Payoff continuity in incomplete information games: a comment," Journal of Economic Theory, Elsevier, vol. 120(2), pages 270-274, February.
    6. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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