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Interactive epistemology in simple dynamic games with a continuum of strategies

Abstract

We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (J Econ Theory 88:188–230, 1999, J Econ Theory 106:356–391, 2002, Res Econ 61:165–184, 2007) from finite dynamic games to all simple games, that is, finite and infinite-horizon multistage games with finite action sets at nonterminal stages and compact action sets at terminal stages. We prove a generalization of Lubin’s (Proc Am Math Soc 43:118–122, 1974) extension result to deal with conditional probability systems and strong belief. With this, we can provide a short proof of the following result: in every simple dynamic game, strong rationalizability characterizes the behavioral implications of rationality and common strong belief in rationality.

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