A conceptually well-founded characterization of iterated admissibility using an “all I know” operator

Joseph Y. Halpern, Rafael Pass

Research output: Contribution to journalConference articlepeer-review

Abstract

Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (IA), also known as 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. In earlier work, we gave a characterization of iterated admissibility using an “all I know” operator, that captures the intuition that “all the agent knows” is that agents satisfy the appropriate rationality assumptions. That characterization did not need complete structures and used probability structures, not LPSs. However, that characterization did not deal with Samuelson’s conceptual concern regarding IA, namely, that at higher levels, players do not consider possible strategies that were used to justify their choice of strategy at lower levels. In this paper, we give a characterization of IA using the all I know operator that does deal with Samuelson’s concern. However, it uses LPSs. We then show how to modify the characterization using notions of “approximate belief” and “approximately all I know” so as to deal with Samuelson’s concern while still working with probability structures.

Original languageEnglish
Pages (from-to)221-232
Number of pages12
JournalElectronic Proceedings in Theoretical Computer Science, EPTCS
Volume297
DOIs
StatePublished - 19 Jul 2019
Externally publishedYes
Event17th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2019 - Toulouse, France
Duration: 17 Jul 201919 Jul 2019

All Science Journal Classification (ASJC) codes

  • Software

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