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Backward Induction is not Robust: The Parity Problem and the Uncertainty Problem

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  • Kilgour, D.M.
  • Brams, S.J.

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).

Suggested Citation

  • Kilgour, D.M. & Brams, S.J., 1996. "Backward Induction is not Robust: The Parity Problem and the Uncertainty Problem," Working Papers 96-21, C.V. Starr Center for Applied Economics, New York University.
  • Handle: RePEc:cvs:starer:96-21
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
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    7. Stuart, Harborne Jr., 1997. "Common Belief of Rationality in the Finitely Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 19(1), pages 133-143, April.
    8. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
    9. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Martin Dufwenberg & Matt Van Essen, 2016. "King of the Hill: Giving Backward Induction its Best Shot," CESifo Working Paper Series 6169, CESifo Group Munich.

    More about this item

    Keywords

    UNCERTAINTY; GAME THEORY; GAMES;

    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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