An
Application of Ramsey Theorem to Stopping Games.

Eran
Shmaya, Eilon Solan and Nicolas Vieille

Games
and Economic Behavior, to appear.

We prove that every two-player non
zero-sum deterministic stopping game with uniformly bounded payoffs admits
a uniform e-equilibrium, for every e
>
0. The proof uses Ramsey Theorem that states that for every coloring of a
complete infinite graph by finitely many colors there is a complete infinite subgraph that is
monochromatic.