Perfect Correlated Equilibria in Stopping Games

We prove that every undiscounted multi-player stopping game in discrete time admits an approximate correlated equilibrium. Moreover, the equilibrium has three appealing properties: trembling-hand perfectness players do not use non-credible threats; normal-form correlation communication is required only before the game starts; uniformness it is an approximate equilibrium in any long enough nitehorizon game and in any discounted game with high enough discount factor.