A Logical Characterization of Iterated Admissibility

Halpern, Joseph Y.
Pass, Rafael
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Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (i.e., iterated deletion of weakly dominated strategies) where uncertainty is represented using LPSs (lexicographic probability sequences). Their characterization holds in a rich structure called a complete structure, where all types are possible. Here, a logical charaacterization of iterated admisibility is given that involves only standard probability and holds in all structures, not just complete structures. A stronger notion of strong admissibility is then defined. Roughly speaking, strong admissibility is meant to capture the intuition that "all the agent knows" is that the other agents satisfy the appropriate rationality assumptions. Strong admissibility makes it possible to relate admissibility, canonical structures (as typically considered in completeness proofs in modal logic), complete structures, and the notion of ``all I know''.
Comment: In Proceedings of Twelfth Conference on Theoretical Aspects of Rationality and Knowledge, 2009, pp. 146-155
Computer Science - Artificial Intelligence, Computer Science - Computer Science and Game Theory, Computer Science - Logic in Computer Science