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An ordinal minimax theorem

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  • Brandt, Felix
  • Brill, Markus
  • Suksompong, Warut

Abstract

In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called weak saddle. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based value.

Suggested Citation

  • Brandt, Felix & Brill, Markus & Suksompong, Warut, 2016. "An ordinal minimax theorem," Games and Economic Behavior, Elsevier, vol. 95(C), pages 107-112.
    • Handle: RePEc:eee:gamebe:v:95:y:2016:i:c:p:107-112
    DOI: 10.1016/j.geb.2015.12.010
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    References listed on IDEAS

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    1. Michel Le Breton & John Duggan, 2001. "Mixed refinements of Shapley's saddles and weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 65-78.
    2. Duggan, John & Le Breton, Michel, 1996. "Dutta's Minimal Covering Set and Shapley's Saddles," Journal of Economic Theory, Elsevier, vol. 70(1), pages 257-265, July.
    3. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    4. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
    5. McKelvey, Richard D. & Ordeshook, Peter C., 1976. "Symmetric Spatial Games Without Majority Rule Equilibria," American Political Science Review, Cambridge University Press, vol. 70(4), pages 1172-1184, December.
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    More about this item

    Keywords

    Zero-sum games; Shapley; Saddles; Minimax theorem;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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