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Teor. Veroyatnost. i Primenen., 1963, Volume 8, Issue 3, Pages 324–327 (Mi tvp4680)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Axiomatic Definition of the Value of a Matrix Game

È. I. Vilkas

Vilnius

Abstract: Let a real function $f$, whose argument is a matrix $A$, satisfy the following axioms:
1. $f(\mathbf{\bar A})\geq(A)$ if $\mathbf{ \bar A}\geq A$;
2. $f(\mathbf{\bar A})=f(A)$ if $A$ differs from $A$ only by a row, which is dominated by others;
3. $f(-A^T)=-f(A)$, the index $T$ stands for transposition;
4. $f(x)\geq x$ for a real number $x$.
Then $f(A)$ is the game value function. Axioms $1$$4$ are independent. Another similar set of axioms is given.

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English version:
Theory of Probability and its Applications, 1963, 8:3, 304–307

Received: 06.03.1963

Citation: È. I. Vilkas, “Axiomatic Definition of the Value of a Matrix Game”, Teor. Veroyatnost. i Primenen., 8:3 (1963), 324–327; Theory Probab. Appl., 8:3 (1963), 304–307

Citation in format AMSBIB
\Bibitem{Vil63}
\by \`E.~I.~Vilkas
\paper Axiomatic Definition of the Value of a Matrix Game
\jour Teor. Veroyatnost. i Primenen.
\yr 1963
\vol 8
\issue 3
\pages 324--327
\mathnet{http://mi.mathnet.ru/tvp4680}
\transl
\jour Theory Probab. Appl.
\yr 1963
\vol 8
\issue 3
\pages 304--307
\crossref{https://doi.org/10.1137/1108035}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. N. Vorob'ev, “The present state of the theory of games”, Russian Math. Surveys, 25:2 (1970), 77–136  mathnet  crossref  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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