Interactive Epistemology and Solution Concepts for Games with Asymmetric Information

Pierpaolo Battigalli (), Alfredo Di Tillio, Edoardo Grillo and Antonio Penta ()

No 340, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

Abstract: This paper characterizes solution concepts for games with asymmetric information by means of expressible epistemic assumptions, i.e. events in the universal type space generated by primitive uncertainty about the players' payoff-relevant and payoff-irrelevant information and actions. Interim correlated rationalizability (Dekel et al., Theoretical Econ., 2007) is characterized by rationality and common belief in rationality. Delta-rationalizability (Battigalli and Siniscalchi, Advances Theoretical Econ., 2003) is characterized by (i) rationality, (ii) the restrictions Delta on first-order beliefs, and (iii) common belief in (i) and (ii). Assuming a type space where higher order beliefs are determined by the players' payoff-relevant and payoff-irrelevant information, as is the case in most economic models, interim correlated rationalizability coincides with Delta-rationalizability, provided that Delta is derived by the type space. Moreover, in that special case, rationalizability in the interim strategic form — equivalent to interim independent rationalizability — also coincides with Delta-rationalizability, when Delta requires, in addition, independence between the state of nature and the opponent's action, conditional on the opponent's information. Finally, the paper introduces a new notion of ex ante correlated rationalizability — to be applied to the ex ante strategic form, appropriate to analyze asymmetric information about an initial chance move. It is proved that this ex ante notion is fully equivalent to interim correlated rationalizability.

Date: 2008
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