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Bounded memory and incomplete information

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  • Sperisen, Benjamin

Abstract

This paper studies incomplete information games where players observe only a summary statistic of the history, including reputation games as a special case. A recursive characterization of the equilibrium payoff set is derived for the case where time is observable, relating it to a self-generating set of tuples that capture equilibrium behavior and payoffs. With unobservable time, equilibria have a particularly simple interpretation as self-generating points. The tools are applied to a product choice game where the firm may be an “honest” commitment type and consumers have 1-period memory with imperfect monitoring, solving for the worst equilibrium payoff. The recursive algorithm shows that the observable-time game allows lower equilibrium payoffs due to non-stationary behavior.

Suggested Citation

  • Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:382-400
    DOI: 10.1016/j.geb.2018.01.004
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    1. Liu, Jia-Cai & Sheu, Jiuh-Biing & Li, Deng-Feng & Dai, Yong-Wu, 2021. "Collaborative profit allocation schemes for logistics enterprise coalitions with incomplete information," Omega, Elsevier, vol. 101(C).
    2. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.

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    More about this item

    Keywords

    Bounded memory; Incomplete information; Reputation; Product choice game;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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