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Third Down with a Yard to Go: The Dixit-Skeath Conundrum on Equilibria in Competitive Games

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Listed:
  • Simon Grant

    (Australian National University)

  • Atsushi Kajii

    (University of Tsukuba)

  • Ben Polak

    (Yale University)

Abstract

In strictly competitive games, equilibrium mixed strategies are invariant to changes in the ultimate prizes. Dixit and Skeath argue that this seems counter-intuitive, and it is a challenge to the expected utility theory. We show that this invariance is robust to dropping the independence axiom, but is removed if we drop the reduction axiom. The conditions on the resulting recursive expected-utility model to get the desired outcome are analogous to conditions used in the standard model of comparative statics under risk.

Suggested Citation

  • Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Third Down with a Yard to Go: The Dixit-Skeath Conundrum on Equilibria in Competitive Games," Econometric Society World Congress 2000 Contributed Papers 0222, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0222
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    References listed on IDEAS

    as
    1. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1998. "Intrinsic Preference for Information," Journal of Economic Theory, Elsevier, vol. 83(2), pages 233-259, December.
    2. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    3. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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