Question a;

1. Consider the following (simultaneous) game of chicken. This is a game in which two players drive cars at each other. The first to swerve away and slow down loses and is humiliated as the "chicken"; if neither player swerves, the result is a potentially fatal head-on collision. The principle of the game is to create pressure until one person backs down. Call s the probability that player 1 swerves, 1 - s the probability that player 1 drives straight, S the probability that Player 2 swerves, and 1 - S the probability that Player 2 drives straight. Compute all the pure-strategy and mixed strategy equilibria. (20 points) 1\\2 Swerving Driving Straight Swerving 0.0 -1, 1 Driving Straight 1, -1 -10, -10 2. Now assume that the game is played sequentially, with player 1 moving first and deciding whether to Swerve or Drive Straight, and player 2 moving second after observing what player 1 did, and deciding also whether to Swerve or Drive Straight. (I know, this makes for a boring game of chicken) Write the decision tree for this game, and find all the pure-strategy Subgame-Perfect Equilibria. In particular, write down the Subgame-Perfect Equilibrium strategies of this dynamic game. How do these equilibria compare to the equilibria of the static game? (15 points)Problem 2. Consumption-Savings Problem with Habit Formation (35 points) In this exercise, we consider the choice of consumption over time. We assume two periods, t = 1 and t = 2. Kim receives no income in period 1 and earns income M in period 2. She can borrow at per-period interest r on each dollar. The peculiarity of this exercise is that Kim's preferences are characterized by habit formation: the more she consumes in the first period, the less she gets utility from consumption in the second period. (This is similar to the addiction problem that you solved in the problem sets). More precisely, Kim has utility function u (c, c) = u(a) tu(c - y1) with 0 0 and u"