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Equivalent Results in MinimaxTheory

Author

Listed:
  • J.B.G. Frenk

    (Econometric Institute, Faculty of Economics, Erasmus University Rotterdam, and Tinbergen Institute)

  • G. Kassay

    (Department of Mathematics, Babes Bolyai University, Cluj)

  • J. Kolumbán

    (Department of Mathematics, Babes Bolyai University, Cluj)

Abstract

In this paper we review known minimax results with applications in game theory and showthat these results are easy consequences of the first minimax result for a two person zero sumgame with finite strategy sets published by von Neumann in 1928. Among these results are thewell known minimax theorems of Wald, Ville and Kneser and their generalizations due to Kakutani,Ky-Fan. Konig. Neumann and Gwinner-Oettli. Actually it is shown that these results form anequivalent chain and this chain includes the strong separation result in finite dimensional spacesbetween two disjoint closed convex sets of which one is compact. To show these implicationsthe authors only use simple properties of compact sets and the well-known Weierstrass Lebesgue lemma.

Suggested Citation

  • J.B.G. Frenk & G. Kassay & J. Kolumbán, 2002. "Equivalent Results in MinimaxTheory," Tinbergen Institute Discussion Papers 02-009/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20020009
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    References listed on IDEAS

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    1. T. Illés & G. Kassay, 1999. "Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 243-257, May.
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