W state and Greenberger–Horne–Zeilinger state in quantum three-person prisoner's dilemma

Abstract It is well known that entangled three particles have two different types of state: W state and Greenberger–Horne–Zeilinger (GHZ) state. When we introduce entanglement to three-person prisoner's dilemma, it is found that if the initial state is W state, the players prefer to form a three-person coalition which can gain the largest payoffs for every player. It is also found that the players prefer to form a two-person coalition and the members of the coalition will gain larger payoffs than the third person if the initial state is GHZ state. From this quantum game we can see the difference between W state and GHZ state clearly.