Geodesic
Axiomatic Definition of the Value of a Matrix Game
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 324-327

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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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     author = {\`E. I. Vilkas},
     title = {Axiomatic {Definition} of the {Value} of a {Matrix} {Game}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {3},
     year = {1963},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a8/}
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È. I. Vilkas. Axiomatic Definition of the Value of a Matrix Game. Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 324-327. http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a8/