Iterated elimination procedures

Luo, Xiao, Qian, Xuewen and Qu, Chen (2019) Iterated elimination procedures. Economic Theory . ISSN 0938-2259

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We study the existence and uniqueness (i.e.,order independence) of any arbitrary form of iterated elimination procedures in an abstract environment. By allowing for a transfinite elimination, we show a general existence of the iterated elimination procedure. Inspired by the seminal work of Gilboa, Kalai and Zemel (1990), we identify a fairly weak suffcient condition of Monotonicity* for the order independence of iterated elimination procedure. Monotonicity* requires a monotonicity property along any elimination path. Our approach is applicable to different forms of iterated elimination procedures used in (in)finite games, for example, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, rationalizability, and soon. We introduce a notion of CD* games, which incorporates Jackson's (1992) idea of "boundedness", and show the iterated elimination procedure is order independent in the class of CD* games. In finite games, we also formulate and show an "outcome" order-independence result suitable for Marx and Swinkels's (1997) notion of nice weak dominance.

Item Type: Article
Additional Information: This publication is under Global University Publication Licence.
Keywords: Iterated elimination procedures; order independence; Monotonicity*; CD* games; "outcome" order independence
Schools/Departments: University of Nottingham Ningbo China > Faculty of Humanities and Social Sciences > School of Economics
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Depositing User: Wu, Cocoa
Date Deposited: 08 Oct 2019 00:36
Last Modified: 08 Oct 2019 00:36

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