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A Syntactic Approach to Rationality in Games

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  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994).

Suggested Citation

  • Giacomo Bonanno, 2007. "A Syntactic Approach to Rationality in Games," Working Papers 247, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:247
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    References listed on IDEAS

    as
    1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    4. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    5. LISMONT, Luc & MONGIN, Philippe, 1994. "On the Logic of Common Belief and Common Knowledge," LIDAM Discussion Papers CORE 1994005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    7. Giacomo Bonanno & Klaus Nehring, 1998. "On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games," Theory and Decision, Springer, vol. 45(3), pages 291-295, December.
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    Cited by:

    1. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 24, University of California, Davis, Department of Economics.
    2. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 134, University of California, Davis, Department of Economics.

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