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General Rationalizability and Its Robustness for Strategic Form Games with Incomplete Information

Tai-Wei Hu

No 771, Econometric Society 2004 Far Eastern Meetings from Econometric Society

Abstract: We extend the $\Delta$-rationalizability (see Battigalli and Siniscalchi 2003) to infinite strategic form games with incomplete information. The most important feature of the $\Delta$-rationalizability is that there is no specified epistemic type space \`{a} la Harsanyi. However, we can impose a collection of exogenous restrictions on first order beliefs over payoff types and strategies represented by a collection of correspondences $\Delta$. When $\Delta$ represents only restrictions on beliefs over payoff types, we show that the $\Delta$-rationalizable sets are nonempty under general topological conditions. Robustness with respect to almost common belief for rationality of $\Delta$-rationalizability is established under general conditions by two alternative approaches. We can approximate common belief by finite order of mutual beliefs; we can approximate common belief by common $p$-belief. One important feature of our analysis in the robustness is that in the second approach, different level of belief is allowed for every order of mutual belief among players

Keywords: rationalizable sets; common p-belief; incomplete information; robustness (search for similar items in EconPapers)
JEL-codes: C72 D82 D83 (search for similar items in EconPapers)
Date: 2004-08-11
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