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Kuhn's Equivalence Theorem for Games in Intrinsic Form

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  • Benjamin Heymann

    (CERMICS)

  • Michel de Lara

    (CERMICS)

  • Jean-Philippe Chancelier

    (CERMICS)

Abstract

We state and prove Kuhn's equivalence theorem for a new representation of games, the intrinsic form. First, we introduce games in intrinsic form where information is represented by $\sigma$-fields over a product set. For this purpose, we adapt to games the intrinsic representation that Witsenhausen introduced in control theory. Those intrinsic games do not require an explicit description of the play temporality, as opposed to extensive form games on trees. Second, we prove, for this new and more general representation of games, that behavioral and mixed strategies are equivalent under perfect recall (Kuhn's theorem). As the intrinsic form replaces the tree structure with a product structure, the handling of information is easier. This makes the intrinsic form a new valuable tool for the analysis of games with information.

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  • Benjamin Heymann & Michel de Lara & Jean-Philippe Chancelier, 2020. "Kuhn's Equivalence Theorem for Games in Intrinsic Form," Papers 2006.14838, arXiv.org.
    • Handle: RePEc:arx:papers:2006.14838
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    References listed on IDEAS

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    1. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    2. Carlos Alós-Ferrer & Klaus Ritzberger, 2016. "The Theory of Extensive Form Games," Springer Series in Game Theory, Springer, number 978-3-662-49944-3, June.
    3. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
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