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Zero-sum games with incompletely defined payoff

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It is shown that a saddle-point solution exists in a two-person, zero-sum game whose payoff is given by a matrix which is not completely defined. On the other hand, we show that such games do not always have a value, so that a saddle-point solution is not necessarily an optimal solution.

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This work was supported by the Centre d'Etudes Atomiques, Saclay, France.

Communicated by G. Leitmann

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Sprzeuzkouski, A. Zero-sum games with incompletely defined payoff. J Optim Theory Appl 18, 103–118 (1976). https://doi.org/10.1007/BF00933798

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Key Words

  • Zero-sum games
  • mixed strategies
  • saddle-point solutions
  • optimal strategies