C R,|4,3 5.1 64 2.1 3,4 3.6 R 3.0 4.6 2.8 Normal form with strictly dominant strategies
4,3 5,1 6,4 2,1 3,4 3,6 3,0 4,6 2,8 R1 R2 R3 C1 C2 C3 Normal form with strictly dominant strategies
Rat Clam Rat 3.-3 0.-5 Clam -5,0 The prisoners' dilemma
-3,-3 0,-5 -5,0 -1,-1 Rat Clam Rat Clam The prisoners’ dilemma
Dominant and dominated strategies A strictly dominant strategy for player i is one which maximizes player is payoff regardless of the strategies chosen by is rivals. Formally, si is a strictly dominant strategy for player i if for all Si in Si, T(si, S. >T si, s i), for all possible s co Where s=(S1,S2,…,S1,S+1…,S).This ys that there is no other allowed strategy(s in Si) for player i that gives a greater payof than s regardless of the strategies played by is rivals If all players have a strictly dominant strategy, then we should expect that if they are rational, they will play their strictly dominant strategies
Dominant and dominated strategies • A strictly dominant strategy for player i is one which maximizes player i’s payoff regardless of the strategies chosen by i’s rivals. Formally, si is a strictly dominant strategy for player i if for all si ’ in Si , πi (si , s-i )>πi (si ’ , s-i ), for all possible s-i , where s-i=(s1 , s2 , …, si-1 , si+1, …, sI ). This says that there is no other allowed strategy (si ’ in Si ) for player i that gives a greater payoff than si regardless of the strategies played by i’s rivals (s-i ). • If all players have a strictly dominant strategy, then we should expect that if they are rational, they will play their strictly dominant strategies
The prisoners dilemma Perhaps the most famous game of all is the prisoners'dilemma The dilemma arises because each would be better off if they cooperate Unless there is some way for the prisoners to enforce the agreement the equilibrium outcome Is noncooperative
The prisoners’ dilemma • Perhaps the most famous game of all is the prisoners’ dilemma. • The dilemma arises because each would be better off if they cooperate. • Unless there is some way for the prisoners’ to enforce the agreement, the equilibrium outcome is noncooperative
Noncooperative and cooperative games It is useful to distinguish between noncooperative and cooperative games. If players are able to make binding commitments to each other, then the game is cooperative This distinction matters because in a cooperative game it is assumed that a player will honor agreements that are not incentive compatible-not in their self-interest. In a noncooperative game agreements are not binding, so a player cannot use them as mechanism to commit to ignore her self-interest As a result her opponent knows that an agreement will not change her incentives and behavior
Noncooperative and cooperative games • It is useful to distinguish between noncooperative and cooperative games. If players are able to make binding commitments to each other, then the game is cooperative. This distinction matters because in a cooperative game it is assumed that a player will honor agreements that are not incentive compatible-not in their self-interest. In a noncooperative game agreements are not binding, so a player cannot use them as mechanism to commit to ignore her self-interest. As a result her opponent knows that an agreement will not change her incentives and behavior