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Chess-like Games Are Dominance Solvable in at Most Two Steps

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  • Ewerhart, Christian

Abstract

We show that strictly competitive, finite games of perfect information that may end in one of three possible ways can be solved by applying only two rounds of elimination of dominated strategies.
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  • Ewerhart, Christian, 2000. "Chess-like Games Are Dominance Solvable in at Most Two Steps," Games and Economic Behavior, Elsevier, vol. 33(1), pages 41-47, October.
    • Handle: RePEc:eee:gamebe:v:33:y:2000:i:1:p:41-47
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    References listed on IDEAS

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    1. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-1151, November.
    2. Borgers, Tilman, 1993. "Pure Strategy Dominance," Econometrica, Econometric Society, vol. 61(2), pages 423-430, March.
    3. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
    4. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
    5. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    6. Christian Ewerhart, 1998. "Rationality and the definition of consistent pairs," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 49-59.
    7. Balkenborg, Dieter & Winter, Eyal, 1997. "A necessary and sufficient epistemic condition for playing backward induction," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 325-345, April.
    8. Gretlein, Rodney, J, 1982. "Dominance Solvable Voting Schemes: A Comment," Econometrica, Econometric Society, vol. 50(2), pages 527-528, March.
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    Cited by:

    1. Eli Ben-Sasson & Adam Tauman Kalai & Ehud Kalai, 2006. "An Approach to Bounded Rationality," Discussion Papers 1439, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Ewerhart, Christian, 2002. "Backward Induction and the Game-Theoretic Analysis of Chess," Games and Economic Behavior, Elsevier, vol. 39(2), pages 206-214, May.
    3. Ewerhart, Christian, 2002. "Iterated Weak Dominance in Strictly Competitive Games of Perfect Information," Journal of Economic Theory, Elsevier, vol. 107(2), pages 474-482, December.
    4. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 132-143, August.
    5. Bo Chen & Rajat Deb, 2018. "The role of aggregate information in a binary threshold game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 381-414, October.
    6. Osterdal, Lars Peter, 2005. "Iterated weak dominance and subgame dominance," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 637-645, September.
    7. V. P. Crawford, 2014. "Boundedly rational versus optimization-based models of strategic thinking and learning in games," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    8. Matros, Alexander, 2018. "Lloyd Shapley and chess with imperfect information," Games and Economic Behavior, Elsevier, vol. 108(C), pages 600-613.
    9. Subhasish Dugar & Haimanti Bhattacharya, 2008. "The Power of Reasoning: Experimental Evidence," Working Paper Series, Department of Economics, University of Utah 2008_20, University of Utah, Department of Economics.

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