Two criminals have been caught by the police. Because of lack of evidence the prosecution needs a confession to convict. If no confession ensures, they will be charged and convinced for a minor offense earning them one year less than a conviction for the main crime. The prosecutor offers each prisoner the following deal. If she confesses, and the other does not, she will get three years off her sentence whereas the other prisoner will get an extra year in prison. If both confess, they will be punished according to the law (no reductions). This story easily translates into the following strategic form game

hN; X; A1, A2; (u1, u2)i with N {1, 2} is the set of players;

A1 {C, N} A2 is the set of strategies common to both players, where C implies "confess", and N implies "not to confess".

Finally, players' payoff functions (u1, u2) are specified as follows:

u1 (C, C) = 1.5; u1 (N,C) = 2; u1 (C, N)=0; u1 (N,N) = 0.5; u2 (C, C) = 1.5; u2 (N,C)=0; u2 (C, N) = 2; u2 (N,N) = 0.5.

(1) Draw the game matrix of this game.

(2) Is there a dominant strategy equilibrium of this game? If so, write down all of dominant strategy equilibria in this game. If no, write down the reason why no dominant strategy equilibrium exists.