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 five appealing properties: (1) “Trembling-hand” perfectness - players do not use non-credible threats; (2) Normal-form correlation - communication is required only before the game starts; (3) Uniformness - it is an approximate equilibrium in any long enough finite-horizon game and in any discounted game with high enough discount factor; (4) Universal correlation device -the device does not depend on the specific parameters of the game. (5) Canonical - the signal each player receives is equivalent to the strategy he plays in equilibrium