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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).

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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 71.

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Length: 22
Date of creation: 27 Jan 2007
Date of revision:
Handle: RePEc:cda:wpaper:07-1

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Related research

Keywords: rationality; common belief; rationalizability; dominated strategies; game logic; frame characterization;

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References

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  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. 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.
  3. LISMONT, Luc & MONGIN, Philippe, 1994. "On the Logic of Common Belief and Common Knowledge," CORE Discussion Papers 1994005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
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Cited by:
  1. Johan Van Benthem & Eric Pacuit & Olivier Roy, 2011. "Toward a Theory of Play: A Logical Perspective on Games and Interaction," Games, MDPI, Open Access Journal, vol. 2(1), pages 52-86, February.
  2. Bonanno, Giacomo, 2008. "Non-cooperative Game Theory," Working Papers 08-6, University of California at Davis, Department of Economics.
  3. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
  4. Emiliano Lorini & François Schwarzentruber, 2010. "A Modal Logic of Epistemic Games," Games, MDPI, Open Access Journal, vol. 1(4), pages 478-526, November.

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