An application of Ramsey theorem to stopping games

Nicolas Vieille (1) , Eran Shmaya , Eilon Solan (2)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 TAU - Tel Aviv University

We prove that every two-player nonzero-sum deterministic stopping game with uniformly bounded payoffs admits an var epsilon-equilibrium, for every var epsilon>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.

Keywords: Nonzero-sum stopping games; Ramsey Theorem; Equilibrium payoff

Domains: Economy and decision science

Nicolas Vieille, Eran Shmaya, Eilon Solan. An application of Ramsey theorem to stopping games. Games and Economic Behavior / Games and Economic Behaviour, 2003, Vol.42,n°2, pp.300-306. ⟨10.1016/S0899-8256(02)00539-0⟩. ⟨hal-00464974⟩