Journal
GAMES AND ECONOMIC BEHAVIOR
Volume 77, Issue 1, Pages 21-40Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.geb.2012.08.012
Keywords
Epistemic game theory; Admissibility; Iterated weak dominance; Common knowledge; Rationality; Completeness
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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) imply S-infinity 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 for S-infinity W and IA. (c) 2012 Elsevier Inc. All rights reserved.
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