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Elimination of dominated strategies and inessential players

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  • Mamoru Kaneko
  • Shuige Liu

Abstract

We study the process, called the IEDI process, of iterated elimination of (strictly) dominated strategies and inessential players for finite strategic games. Such elimination may reduce the size of a game considerably, for example, from a game with a large number of players to one with a few players. We extend two existing results to our context; the preservation of Nash equilibria and order-independence. These give a way of computing the set of Nash equilibria for an initial situation from the endgame. Then, we reverse our perspective to ask the question of what initial situations end up at a given final game. We assess what situations underlie an endgame. We give conditions for the pattern of player sets required for a resulting sequence of the IEDI process to an endgame. We illustrate our development with a few extensions of the battle of the sexes.

Suggested Citation

  • Mamoru Kaneko & Shuige Liu, 2015. "Elimination of dominated strategies and inessential players," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(1), pages 33-54.
    • Handle: RePEc:wut:journl:v:1:y:2015:p:33-54:id:1144
    DOI: 10.5277/ord150103
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    References listed on IDEAS

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    1. Ehud Kalai & Eitan Zemel, 1988. "On The Order of Eliminating Dominated Strategies," Discussion Papers 789, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Krzysztof R. Apt, 2011. "Direct proofs of order independence," Economics Bulletin, AccessEcon, vol. 31(1), pages 106-115.
    3. Mamoru Kaneko & J. Jude Kline, 2015. "Understanding the Other Through Social Roles," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-31.
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    Cited by:

    1. Virtue Ekhosuehi, 2018. "On the one-shot two-person zero-sum game in football from a penalty kicker’s perspective," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(3), pages 17-27.

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