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Dominance rationality: A unified approach

John Hillas and Dov Samet

Games and Economic Behavior, 2020, vol. 119, issue C, 189-196

Abstract: There are four types of dominance depending on whether domination is strict or weak and whether the dominating strategy is pure or mixed. Letting d vary over these four types of dominance, we say that a player is d-dominance rational when she does not play a strategy that is d-dominated relative to what she knows. For weak dominance by a mixed strategy, Stalnaker (1994) introduced a process of iterative maximal elimination of certain profiles that we call here flaws. We define here, analogously, d-flaws for each type of dominance d, and show that for each d, iterative elimination of d-flaws is order independent. We then show that the characterization of common knowledge of d-dominance rationality is the same for each d. A strategy profile can be played when d-dominance rationality is commonly known if and only if it survives an iterative elimination of d-flaws.

Keywords: Dominance rationality; Strict dominance; Weak dominance; Order independence; Flaws; Common knowledge of rationality; Iterative elimination (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.geb.2019.11.001

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