(b) Consider the two-period repeated game in which this stage game is played twice. Suppose the repeated game payo¤s are simply the sum of the payo¤s in each of the two periods. Then, is there a subgame perfect Nash equilibrium of this repeated game in which (A,X) is played in the …rst period? If so, fully describe the equi- librium. If not, explain why.
You and your n − 1 roommates (n ≧ 2) each have five hours of free time that could be used to clean your apartment. You all dislike cleaning, but you all like having a clean apartment: each person i’s payoff is the total hours spent (by everyone) cleaning, minus a number c (> 0) times the hours spent individually cleaning. That is,
payoff) while M gives 1 irrespective of player 1’s strategy.
Therefore, M is eliminated by mixing L and R .
After eliminating M , we can further eliminate D (step 2) and L
(step 3), eventually picks up ( U , R ) as a unique outcome.
e z . The prices of the three goods are given by (p, q, 1) and the consumer’s wealth is given by ω.
(a) Formulate the utility maximization problem of this consumer.
(b) Note that this consumer’s preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).