The classic game theory problem is the "prisoners' dilemma." In this game, two criminals are apprehended, but the police have only got circumstantial evidence to prosecute them for a small crime, without having the evidence to prosecute them for the major crime of which they are suspected. The interrogators then pose incentives to the crooks-incentives to talk. The crooks are put in separate jail cells and have the option to confess or deny. Their payoff depends upon what course of action each adopts. The payoff matrix is given below. The first element in each box is the payoff (years in jail) to the player in the left column, and the second element is the payoff to the player in the top row.
(a) Does a "dominant strategy" present itself for each or both of the crooks?
(b) What is the Nash equilibrium to this game?
(c) Is the Nash equilibrium unique?
(d) Was it important for the police to place the crooks in separate cells?