An Application of Ramsey Theorem to Stopping Games

E. Shmaya, E. Solan, N. VIEILLE

Games and Economic Behavior

February 2003, vol. 42, n°2, pp.300-306

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

We prove that every two-player nonzero-sum deterministic stopping game with uniformly bounded payoffs admits an 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 which is monochromatic.