Forcing Iterated Admissibility in Strategic Belief Models

TL;DR

This paper provides a new epistemic characterization of iterated admissibility in strategic belief models, using a weaker completeness notion and Cohen's forcing technique to address limitations in existing models.

Contribution

It introduces a weaker completeness condition and employs Cohen's forcing to characterize strategies satisfying $R extinfty AR$ in a general setting.

Findings

Characterizes IA as strategies satisfying $R extinfty AR$ under weaker completeness.

Introduces generic types and uses Cohen's forcing in epistemic game theory.

Addresses limitations of previous models with continuous types.

Abstract

Iterated admissibility (IA) can be seen as exhibiting a minimal criterion of rationality in games. In order to make this intuition more precise, the epistemic characterization of this game-theoretic solution has been actively investigated in recent times: it has been shown that strategies surviving m+1 rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality (RmAR) in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, $R\infty AR$, might not be satisfied by any state in the epistemic structure, if the class of types is complete and the types are continuous. In this paper we introduce a weaker notion of completeness which is nonetheless sufficient to characterize IA in a highly general way as the class of strategies that indeed satisfy $R\infty AR$. The key methodological innovation involves defining a new notion of generic types and employing these in conjunction with Cohen's technique of forcing.