Geodesic
Minimax Theorems for Games on Unit Square
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 554-555

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We consider a class of infinite games with unbounded cores and establish the existence of their value. It is shown that a game with the core $$ K(x,y)=\begin{cases} L(x,y),, \\ \varphi(x),=y, \\ M(x,y),>y, \end{cases} $$ where the functions $L$ and $M$ are defined and continuous on the triangles $0\leqq x\leqq y\leqq 1$, $0\leqq y\leqq x\leqq 1$, respectively, the function $\varphi$ is arbitrary and $L(0,0)\geqq M(0,0)$, $L(1,1)\leqq M(1,1)$, is a game with value. 
@article{TVP_1964_9_3_a15,
     author = {E. B. Janovskaya},
     title = {Minimax {Theorems} for {Games} on {Unit} {Square}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {554--555},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a15/}
}
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E. B. Janovskaya. Minimax Theorems for Games on Unit Square. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 554-555. http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a15/