Geodesic
On games on the unit square with a~``roof'' payoff
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 138-149

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This paper describes all the optimal strategies of players on the unit square witk the payoff $$ K(x,y)= \begin{cases} 1+\frac1\delta(x-y)\text{if}\quad|x-y|\le\delta,\quad x\le y, \\ 1+\frac1\delta(y-x)\text{if}\quad|x-y|\le\delta,\quad x>y, \\ p\text{if}\quad|x=y|>\delta, \end{cases} $$ where $\delta>0$. 
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     author = {G. N. Dyubin},
     title = {On games on the unit square with a~``roof'' payoff},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {138--149},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {1968},
     language = {ru},
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}
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G. N. Dyubin. On games on the unit square with a~``roof'' payoff. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 138-149. http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a9/