Correlated equilibrium in quitting games

A quitting game is a sequential game where each player has two actions: to continue or to quit. The game continues as long as all players decide to continue. The moment at least one player decides to quit, the game terminates. The terminal payoff depends on the subset of players who quit at the terminating stage. If the game continues forever, then the payoff for the players is some fixed-payoff vector. We prove that every quitting game admits a correlated uniform epsilon-equilibrium – a uniform epsilon-equilibrium in an extended game that includes a correlation device that sends one signal to each player before start of play.