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.