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Uncertainty Aversion and Backward Induction

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  • Jorn Rothe

    (London School of Economics)

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    Abstract

    In the context of the centipede game this paper discusses a solution concept for extensive games that is based on subgame perfection and uncertainty aversion. Players who deviate from the equilibrium path are considered non- rational. Rational players who face non-rational opponents face genuine uncertainty and may have non-additive beliefs about their future play. Rational players are boundedly uncertainty averse and maximise Choquet expected utility. It is shown that if the centipede game is sufficiently long, then the equilibrium strategy is to play `Across' early in the game and to play `Down' late in the game.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1610.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:1610

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    1. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    2. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
    3. Basu, Kaushik, 1988. "Strategic irrationality in extensive games," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 247-260, June.
    4. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
    7. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    8. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    9. Dow, James & Werlang, Sérgio Ribeiro da Costa, 1992. "Nash equilibrium under knightian uncertainty: breaking-down backward induction," Economics Working Papers (Ensaios Economicos da EPGE) 186, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    10. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
    11. Sarin, Rakesh & Wakker, Peter, 1994. "A General Result for Quantifying Beliefs," Econometrica, Econometric Society, vol. 62(3), pages 683-85, May.
    12. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
    13. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
    14. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    15. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    16. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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