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Finite Reasoning Procedures for Dynamic Games

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Models of Strategic Reasoning

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8972))

Abstract

In this chapter we focus on the epistemic concept of common belief in future rationality (Perea [37]), which describes a backward induction type of reasoning for general dynamic games. It states that a player always believes that his opponents will choose rationally now and in the future, always believes that his opponents always believe that their opponents choose rationally now and in the future, and so on, ad infinitum. It thus involves infinitely many conditions, which might suggest that this concept is too demanding for real players in a game. In this chapter we show, however, that this is not true. For finite dynamic games we present a finite reasoning procedure that a player can use to reason his way towards common belief in future rationality.

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Acknowledgments

I would like to thank the participants at the Workshop on Modeling Strategic Reasoning in Leiden (2012) for many useful comments. I am also grateful to two anonymous referees for valuable suggestions.

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Authors and Affiliations

  1. EpiCenter and Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands

    Andrés Perea

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  1. Andrés Perea
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Correspondence to Andrés Perea .

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Editors and Affiliations

  1. Inst for Logic Language & Computation, University of Amsterdam, Amsterdam, Noord-Holland, The Netherlands

    Johan van Benthem

  2. Indian Statistical Institute, Chennai, Tamil Nadu, India

    Sujata Ghosh

  3. Faculty of Math & Natural Sci, University of Groningen, Groningen, Groningen, The Netherlands

    Rineke Verbrugge

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Perea, A. (2015). Finite Reasoning Procedures for Dynamic Games. In: van Benthem, J., Ghosh, S., Verbrugge, R. (eds) Models of Strategic Reasoning. Lecture Notes in Computer Science(), vol 8972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48540-8_3

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  • DOI: https://doi.org/10.1007/978-3-662-48540-8_3

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