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Logics for Dynamic Epistemic Behavioral Strategies

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Book cover Structural Analysis of Non-Classical Logics

Part of the book series: Logic in Asia: Studia Logica Library ((LIAA))

Abstract

This paper shows how the probabilistic logic of communication and change can be used to reason about finite extensive-form games with incomplete or imperfect information and with probabilistic nature moves. The results of probabilistic behavioral strategies can be expressed, as well as the results of strategies that are sensitive not also just to the history of the game, but also to the beliefs of agents. Using this logic, game-theoretic concepts, such as best response, Nash equilibrium, and rationality can be expressed with respect to a finite set of possible strategies. Extensions to the logic are also proposed to allow for the comparison between one strategy and infinitely many others, thus providing less restricted expressions for best response, Nash equilibrium, and rationality.

The research by this author has been made possible by VIDI grant 639.072.904 of the Netherlands Organization of Scientific Research (NWO).

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Notes

  1. 1.

    We restrict to \(\mathfrak {E}^o(\mathcal {F})\) for simplicity. Without restricting to ordinary behavioral strategies, we might still want to impose further restrictions on \(\approx _a\) concerning whether agents b other than a must retain the same probabilistic beliefs about other agents’ moves. Such a restriction would be significant in how their epistemic behavioral strategies are played.

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Acknowledgments

I would like to thank the reviewer for the valuable comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, California State University Long Beach, 1250 Bellflower Blvd, Long Beach, CA 90840, USA

    Joshua Sack

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  1. Joshua Sack
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Correspondence to Joshua Sack .

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Editors and Affiliations

  1. Department of Philosophy, National Taiwan University, Taipei, Taiwan

    Syraya Chin-Mu Yang

  2. Department of Philosophy, National Taiwan University, Taipei, Taiwan

    Duen-Min Deng

  3. Department of Philosophy, University of California, Davis, CA, Australia

    Hanti Lin

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Sack, J. (2016). Logics for Dynamic Epistemic Behavioral Strategies. In: Yang, SM., Deng, DM., Lin, H. (eds) Structural Analysis of Non-Classical Logics. Logic in Asia: Studia Logica Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48357-2_8

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