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Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem

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  • Steven Brams
  • D. Kilgour

Abstract

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem).
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  • Steven Brams & D. Kilgour, 1998. "Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem," Theory and Decision, Springer, vol. 45(3), pages 263-289, December.
    • Handle: RePEc:kap:theord:v:45:y:1998:i:3:p:263-289
    DOI: 10.1023/A:1005038921033
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    Cited by:

    1. Dufwenberg, Martin & Van Essen, Matt, 2018. "King of the Hill: Giving backward induction its best shot," Games and Economic Behavior, Elsevier, vol. 112(C), pages 125-138.
    2. Dufour, J.M., 2000. "Econometrie, theorie des tests et philosophie des sciences," Cahiers de recherche 2000-14, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Bossert, Walter & Brams, Steven J. & Kilgour, D. Marc, 2002. "Cooperative vs non-cooperative truels: little agreement, but does that matter?," Games and Economic Behavior, Elsevier, vol. 40(2), pages 185-202, August.
    4. Brams Steven J., 2000. "Game Theory: Pitfalls and Opportunities in Applying It to International Relations," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 6(2), pages 1-11, April.
    5. Dao-Zhi Zeng & Liping Fang & Keith Hipel & D. Kilgour, 2004. "Policy Stable States in the Graph Model for Conflict Resolution," Theory and Decision, Springer, vol. 57(4), pages 345-365, December.
    6. Edwin Woerdman, 2000. "Rationality And Stability In The Theory Of Moves," Rationality and Society, , vol. 12(1), pages 67-86, February.
    7. Brams, S. J. & Kilgour, M. D., 2001. "Games That End in a Bang or a Whimper," Working Papers 01-05, C.V. Starr Center for Applied Economics, New York University.

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    More about this item

    Keywords

    Backward induction; Bounded rationality; Continuation probability; Infinite horizon; Parity; Uncertainty;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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