4. The following scenario will probably be familiar to anyone who watches Law and Order, TVs longest-running crime series (cue dun dun sound). As many of you are probably aware, however, certain types of criminals in the real world rarely talk or rat out their accomplices. In particular, it is well known that members of the Mafia or Cosa Nostra rarely provide incriminating evidence against their accomplices. Why is this? The answer is that the Mafia organization imposes a cost (c), often physical and deadly, on anyone who talks to the police. This additional cost changes the structure of the strategic situation in which the two prisoners find themselves. Rather than playing the traditional Prisoners Dilemma Game, we can think that the prisoners are playing a Mafia Game like the one in Figure 1. (a) Solve the game in Figure 2 for any (pure strategy) Nash equilibria assuming that c = 0. What type of game does this resemble? [7 points] b) Given the payoffs in the Mafia Game, what is the minimum cost, c, that the Mafia needs to impose on members who talk in order for the Nash equilibrium to be (quiet; quiet)? Explain your answer, and be sure to show your work. [7 points] (c) The role of the Mafia can be thought of as that of a third-party enforcer. What do we mean by that? How is the role that the Mafia plays in this game related to the role that the state plays in the Civil Society game we examined in class? [5 points]

Group B acquiesce challenge acquiesce 2,2 2,1 Group A challenge 1,2 7,7 Figure 2: Falcone and Maroni Got Caught Maroni quiet talk quiet 30, 30 10,40 -C Falcone talk 40 c, 10 20 c, 20 - C M Figure 1: Group A and Group B decide if they are in sync in the Coordination and Democracy game Group B acquiesce challenge acquiesce 2,2 2,1 Group A challenge 1,2 7,7 Group B acquiesce challenge acquiesce 2,2 2,1 Group A challenge 1,2 7,7 Figure 2: Falcone and Maroni Got Caught Maroni quiet talk quiet 30, 30 10,40 -C Falcone talk 40 c, 10 20 c, 20 - C M Figure 1: Group A and Group B decide if they are in sync in the Coordination and Democracy game Group B acquiesce challenge acquiesce 2,2 2,1 Group A challenge 1,2 7,7