Respond to each classmate 100 words a piece Classmate 1 In the game of prisoner’s dilemma, if both the players, Jesse and Frank stay quiet, they would get the lowest punishment. However, looking at each individual it changes things, it isn’t the least punishment. If Jesse plays “Confess,” Frank chooses “Confess” (because −5 is better than −10), and if Jesse plays “Stay Mum,” Frank chooses “Stay Mum.” The DA would like to change the game to get Frank and Jesse to confess for sure. She does this by increasing the reward to confessing. The DA promises Jesse that if he confesses while Frank stays mum, she will let Jesse go free. She makes the same offer to Frank. In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players and no player has anything to gain by changing only their own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who applied it to competing firms choosing outputs. The simple insight underlying Nash’s idea is that one cannot predict the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do taking into account what she/he expects the others to do. Nash equilibrium requires that their choices be consistent: no player wishes to undo their decision given what the others are deciding. Staying mum is definitely the best option for both Jesse and Frank. Classmate 2 Jesse and Frank can both start off by planning to Stay Mum. If this ends up happening then they will each earn a payoff of -2. This will change if one does it and the other does not. If Jesse thinks that Frank will choose to Stay Mum and confesses then she will earn a greater payoff (0>-2). Similarly, anticipating that Jesse will choose to Stay Mum, Frank will Confess and earn a greater payoff (0 > -2). Therefore, both players will never choose Stay Mum while anticipating that the other player is going to choose Stay Mum. Now, Frank knows that Jesse is rational and will not choose Stay Mum while anticipating that Frank will choose Stay Mum. Therefore, Frank will use Jesse’s rationality to infer that Jesse will anticipate Frank to Confess. Frank’s best response to Jesse expecting Frank to Confess is to choose Confess and earn the greater payoff (-5 > -10). A symmetrical logic applies to Jesse. Hence, Jesse’s best response to Frank expecting Jesse to Confess is to choose Confess and earn the greater payoff (-5 > -10). The game has only one equilibrium strategy profile: (Confess, Confess). Both Jesse and Frank players can do better by choosing Stay Mum. However, the possibility of the other player choosing to Confess deters both players from choosing the socially optimal strategy profile–which is the defining feature of a Prisoner’s Dilemma. Both players end up choosing their dominant strategies and the outcome of the game is Pareto inefficient.