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manuscripta mathematica

, Volume 29, Issue 2–4, pp 277–294 | Cite as

Minimaxtheoreme und das Integraldarstellungsproblem

  • Jürgen Kindler
Article

Abstract

In the present paper conditions for the strict determinateness of two-person zero-sum games are considered. In order to get such ‘minimax theorems’ we first study games with concave-convex pay-off function. If a game does not have this convexity property one usually passes to a mixed extension where both players are allowed to use probability measures (‘σ-additive randomizations’) or, more generally, probability contents (‘finitely additive randomizations’) as mixed strategies. By means of a very general minimax theorem for such finitely additive randomizations it can be shown that the problem of strict determinateness of σ-additive randomizations is equivalent to an integral representation problem. The latter is investigated in the last paragraph.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jürgen Kindler
    • 1
  1. 1.Institut für Mathematische StatistikUniversität KarlsruheKarlsruhe

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