B. Two prisoners, Aidan and Jack. are being interrogated. Each is told that if they confess to running a campus center cup theft ring, they will be expelled for one semester. If one person does not confess, but the other person does. then the one who does not confess will be expelled for three semesters. If neither confesses. they will both go free. ASSume that expulsion leads to a loss of utility for both persons. (1) a. Set up the payoff matrix that describes this prisoners' dilemma. Are there any Nash equilibria in this game? Is there an equilibrium in dominant strategies? b. Explain what a minimax strategy is. If both players use the minimax strategy. where will they end up? (2) Now assume Aidan gets to either c0nfess or deny rst. and then Jack gets to choose what to do after being told what Aidan has done. a. Has the payoff matrix changed? b. Write down the game in extensive form. Now where will the players end up? c. Would your answer to b. change if Jack went first? (3) A new interrogator comes in and changes the rules of the game: It Jack confesses, he gets off free. The other rules stay the same as for (1). a. Write down the new payoff matrix. Are there any Nash equilibria? Is there an equilibrium in dominant strategies? b. Would the game end up differently if Aidan went first and Jack were told what he had chosen before he decided what to do? (4) The new interrogator changes the rules again: Now if both confess, they get off free. The other rules stay the same as for (1). a. Write down the new payoff matrix. Are there any Nash equilibria? Is there an equilibrium in dominant strategies? b. What kind of strategy should each person pursue in this game? C. There are two persons, A and B. and two goods. 1 and 2. , .. . . 1 2 . 1 2 , . 1 2 . 1 Person As utility function is UA(XA .XA} = mrn()t , xA }. and Bs Is Uth XI?) = min()( B (1) a. Draw an Edgeworth box if M; + W1B ) = (wi + w; ) = 3. Which point is B's preferred point? Which is A's? 2 FXB }' b. If A's endowment is W1 = 6. Wi = 2, mark endowment point W. (2) a. Draw the indifference curves that go through W and indicate the set of feasible allocations. b. Given W. what Pareto-optimal allocation would A choose? What would B choose? (3) a. Show which points lie on the contract curve. b. Show which points on the contract curve are in the set of feasible allocations. (4) a. If P1 = 1 and P2 = 1, draw the budget line through W. b. Show the market equilibrium X and the related indifference curves