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Admissibility and event-rationality

Barelli, M. and Galanis, S. ORCID: 0000-0003-4286-7449 (2013). Admissibility and event-rationality. Games and Economic Behavior, 77(1), pp. 21-40. doi: 10.1016/j.geb.2012.08.012

Abstract

We develop an approach to providing epistemic conditions for admissible behavior in games. Instead of using lexicographic beliefs to capture infinitely less likely conjectures, we postulate that players use tie-breaking sets to help decide among strategies that are outcome-equivalent given their conjectures. A player is event-rational if she best responds to a conjecture and uses a list of subsets of the other players' strategies to break ties among outcome-equivalent strategies. Using type spaces to capture interactive beliefs, we show that event-rationality and common belief of event-rationality (RCBER) implyS ∞W, the set of admissible strategies that survive iterated elimination of dominated strategies. By strengthening standard belief to validated belief, we show that event-rationality and common validated belief of event-rationality (RCvBER) imply IA, the iterated admissible strategies. We show that in complete, continuous and compact type structures, RCBER and RCvBER are nonempty, hence providing epistemic criteria forS ∞W and IA.

Publication Type: Article
Additional Information: © Elsevier, 2013. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Epistemic game theory; Admissibility; Iterated weak dominance; Common Knowledge; Rationality; Completeness
Subjects: H Social Sciences > HB Economic Theory
Departments: School of Arts & Social Sciences > Economics
URI: http://openaccess.city.ac.uk/id/eprint/21338
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