Proof-theoretic analysis of rationality for strategic games with arbitrary strategy sets

Authors:
Jonathan A. Zvesper;Krzysztof R. Apt
Affiliations:
Oxford University, Computing Laboratory, Oxford, UK;Centre for Mathematics and Computer Science, Amsterdam, The Netherlands and University of Amsterdam, Amsterdam, The Netherlands
Venue:
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
Year:
2010

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Abstract

In the context of strategic games, we provide an axiomatic proof of the statement (Imp) Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. Rationality here means playing only strategies one believes to be best responses. This involves looking at two formal languages. One, LO, is first-order, and is used to formalise optimality conditions, like avoiding strictly dominated strategies, or playing a best response. The other, Lν, is a modal fixpoint language with expressions for optimality, rationality and belief. Fixpoints are used to form expressions for common belief and for iterated elimination of non-optimal strategies.