Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information

Pierpaolo Battigalli () and Andrea Prestipino

The B.E. Journal of Theoretical Economics, 2013, vol. 13, issue 1, 79-130

Abstract: Abstract: We analyze forward-induction reasoning in games with asymmetric information assuming some commonly understood restrictions on beliefs. Specifically, we assume that some given restrictions Δ on players’ initial or conditional first-order beliefs are transparent, that is, not only do the restrictions Δ hold but there is also common belief in Δ at every node. Most applied models of asymmetric information are covered as special cases whereby Δ pins down the probabilities initially assigned to states of nature. But the abstract analysis also allows for transparent restrictions on beliefs about behavior, e.g. independence restrictions or restrictions induced by the context behind the game. Our contribution is twofold. First, we use dynamic interactive epistemology to formalize assumptions that capture foward-induction reasoning given the transparency of Δ, and show that the behavioral implications of these assumptions are characterized by the Δ-rationalizability solution procedure of Battigalli (1999, 2003). Second, we study the differences and similarities between this solution concept and a simpler solution procedure put forward by Battigalli and Siniscalchi (2003). We show that the two procedures are equivalent if Δ is “closed under compositions” a property that holds in all the applications considered by Battigalli and Siniscalchi (2003). We also show that when Δ is not closed under compositions, the simpler solution procedure of Battigalli and Siniscalchi (2003) may fail to characterize the behavioral implications of forward-induction reasoning.

Keywords: epistemic game theory; rationalizability; forward induction; transparent restrictions on beliefs (search for similar items in EconPapers)
JEL-codes: C72 C73 D82 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (12)

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Working Paper: Transparent Restrictions on Beliefs and Forward Induction Reasoning in Games with Asymmetric Information (2011)
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DOI: 10.1515/bejte-2012-0005

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