Geodesic
The problem of $\delta$-meeting on a~$3$-dimensional ball
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 198-203

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An infinite non-zero-sum two-person game with payoff function $$ L_{\delta}(x,y)= \begin{cases} 1, \rho(x,y)\le\delta,\\ 0, \rho(x,y)>\delta, \end{cases} \qquad(x\in X,y\in Y) $$ (where $X$, $Y$ are $3$-dimensional unit balls) is considered. A solution of this game for $0,475\delta1$ is given. 
@article{TVP_1978_23_1_a20,
     author = {M. M. Lucenko},
     title = {The problem of $\delta$-meeting on a~$3$-dimensional ball},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {198--203},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a20/}
}
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M. M. Lucenko. The problem of $\delta$-meeting on a~$3$-dimensional ball. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 198-203. http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a20/