game. For example, we let DCC represent the payoff to a defecting player if both opponents cooperate. Note that the first position represents the player under consideration. The second and third positions represent the opponents Another example: CCD represents the payoff to a cooperating player if one opponent cooperates and the other opponent defects. Since we assume a symmetric game matrix CCD could be written as CDC. The choice is arbitrar Now we are ready to discuss the payoffs for the three-player game. We impose three ules( Actually, there is no universal definition for the multi-player prisoner's dilemma The constraints used here represent one possible version of the three-player prisoner's dilemma) 1)Defection should be the dominant choice for each player. In other words, it should always be better for a player to defect, regardless of what the opponents do. This rule gives three constraints DCC>Ccc DDD>CDD DCD>CCD 2)A player should al ways be better off if more of his opponents choose to cooperate This rule gives DCC> DCD>DDD CCc> CCD> CDD 3)If one players choice is fixed, the other two players should be left in a two-player prisoner's dilemma. This rule gives the following constraints: CCD>DDD CCC>DCD CCD、CDD+DCD CCC、CCD+DCC We can satisfy all of these constraints with the following payoffs CDD=0. DDD=1. CCD=2. DCD=3. CCC= 4. DCC=5game. For example, we let DCC represent the payoff to a defecting player if both opponents cooperate. Note that the first position represents the player under consideration. The second and third positions represent the opponents. Another example: CCD represents the payoff to a cooperating player if one opponent cooperates and the other opponent defects. Since we assume a symmetric game matrix, CCD could be written as CDC. The choice is arbitrary. Now we are ready to discuss the payoffs for the three-player game. We impose three rules (Actually, there is no universal definition for the multi-player prisoner's dilemma. The constraints used here represent one possible version of the three-player prisoner's dilemma): 1) Defection should be the dominant choice for each player. In other words, it should always be better for a player to defect, regardless of what the opponents do. This rule gives three constraints: 2) A player should always be better off if more of his opponents choose to cooperate. This rule gives: 3) If one player's choice is fixed, the other two players should be left in a two-player prisoner's dilemma. This rule gives the following constraints: We can satisfy all of these constraints with the following payoffs: CDD = 0, DDD = 1, CCD = 2, DCD = 3, CCC = 4, DCC = 5