Problem
The article "SAC Case Tests a Classic Dilemma" describes how certain aspects of the government's insider trading case against SAC capital resembles the standard prisoner's dilemma game as well as other aspects of the case that do not fit so neatly with the simple model. The article quotes Professor Randal Picker who says, "game theorists will say that if you don't like an outcome you change the rules of the game. You change the payoffs so people see the situation differently. Then, all bets are off." For the purposes of this problem, assume that the two players in the game are Matthew Martoma and Steven A. Cohen and that the options available to them are the same as in the classic prisoner's dilemma: cooperate with the authorities (i.e., confess) or don't. Suppose that you are the lead prosecutor in this case, and you have to decide how much jail time Martoma and Cohen would get in all four of the possible outcomes.
1. Draw a standard 2 × 2 game matrix, well-labeled with each player and each players' set of strategies, and fill in the matrix with a set of payoffs (i.e., jail times) that would yield the standard prisoner's dilemma. That is, where the equilibrium is for both players to confess, but they would both be better off if they both managed to stay silent. (Make sure you are clear as to if the numbers you are putting into your matrix are good or bad for the players.)
2. Draw a second 2 × 2 game matrix with different payoffs such that in equilibrium Mr. Martoma chooses not to confess.