How Quantum Entanglement Helps to Coordinate Non-Communicating Players

We consider a coalitional game with the same payoff for all players. To maximize the payoff, the players need to use one collective strategy, if all players are in certain states, and the other strategy otherwise. The current state of each player changes according to external conditions and is not known to the other players. In one example of such a game, quantum entanglement between players results in the optimal payoff thrice the maximal payoff for unentangled players.