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The Logical Representation of Extensive Games

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  • Bonanno, Giacomo

Abstract

Given an extensive form "G", we associate with every choice an atomic sentence and with every information set a set of well-formed formulas (wffs) of propositional calculus. The set of such wffs is denoted by [Gamma](G). Using the so-called topological semantics for propositional calculus (which differs from the standard one based on truth tables), we show that the extensive form yields a topological model of [Gamma](G), that is, every wff in [Gamma](G), is "true in G". We also show that, within the standard truth-table semantics for propositional calculus, there is a one-to-one and onto correspondence between the set of plays of G and the set of valuations that satisfy all the wffs in [Gamma](G).

Suggested Citation

  • Bonanno, Giacomo, 1993. "The Logical Representation of Extensive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(2), pages 153-169.
    • Handle: RePEc:spr:jogath:v:22:y:1993:i:2:p:153-69
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    Cited by:

    1. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.

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