A syntactic approach to rationality in games with ordinal payoffs

In Giacomo Bonanno, Wiebe van der Hoek & Michael Wooldridge (eds.), Logic and the Foundations of Game and Decision Theory. Amsterdam University Press (2008)
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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). Frame characterization results are also provided.

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2009-01-28

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Giacomo Bonanno
University of California, Davis

References found in this work

Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
On the evaluation of solution concepts.Robert Stalnaker - 1994 - Theory and Decision 37 (1):49-73.
La connaissance commune en logique modale.Luc Lismont - 1993 - Mathematical Logic Quarterly 39 (1):115-130.
On the Logic of Common Belief.Giacomo Bonanno - 1996 - Mathematical Logic Quarterly 42 (1):305-311.

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