Let $(X,d)$ be a compact ultrametric space. Hartig and de Vink considered the following ultrametric on the set $P(X)$ of probability on $X$: $$\hat d(\mu,\nu)=\inf\{r>0:\forall x\in X\;\;\mu(B_r(x))=\nu(B_r(x))\}.$$ One can consider games on $X$ with mixed strategies in $(P(X),\hat d)$.
Problem. (Dis)prove the existence of an equilibrium for such a game.
This problem was posed on 12 March 2022 by Mykhailo Zarichnyi on page 116 of Volume 3 of Lviv Scottish Book.
Prize: A bottle of ``Tuca".
