Econ 521 - Week 13:

Exercise 1 - Asymmetric Information

1. The Market for Lemons

Suppose there are two kinds of used cars in the market: Bad used cars (commonly known as lemons) and good used cars. Used-car owners sell their cars to car dealers, but they are unable to tell the difference between good cars and bad ones. Sellers, on the other hand, know exactly whether their car is a good one or not.

Suppose the quality of the car θ ∼ u[0, 1] and that the seller values the car in v_sθ, whers the buyer in v_bθ, with v_b > v_s > 0.

(a) Determine when is efficient to sell a car when there is no asymmetric information.

(b) Suppose the seller knows θ but the buyer doesn't. When does trade occur? Explain.

(c) Based on (a) and (b) explain what is the effect of asymmetric information.

Exercises 2- Dynamic Games

1. Union bargaining - A firms output is L(100 - L) when it uses L ≤ 50 units of labor, and 2500 when it uses L > 50 units of labor. The price of output is 1. A union that represents workers presents a wage demand (a nonnegative number w), which the firm either accepts or rejects. If the firm accepts the demand, it chooses the number L of workers to employ (which you should take to be a continuous variable, not an integer); if it rejects the demand, no production takes place (L = 0). The firms preferences are represented by its profit; the unions preferences are represented by the value of wL.

(a) Find the subgame perfect equilibrium of the game.

(b) Is there an outcome of the game that both parties prefer to any subgame perfect equilibrium outcome?

(c) Find a Nash equilibrium for which the outcome differs from any subgame perfect equilibrium outcome.

2. The "rotten kid theorem" - A child's action a (a number) affects both her own private income c(a) and her parents income p(a); for all values of a we have c(a) < p(a). The child is selfish: she cares only about the amount of money she has. Her loving parent cares both about how much money she has and how much her child has. Specifically, her preferences are represented by a payoff equal to the smaller of the amount of money she has and the amount of money her child has. The parent may transfer money to the child. First the child takes an action, then the parent decides how much money to transfer. Model this situation as an extensive game and show that in a subgame perfect equilibrium the child takes an action that maximizes the sum of her private income and her parents income. (In particular, the child's action does not maximize her own private income. The result is not limited to the specific form of the parents preferences, but holds for any preferences with the property that a parent who is allocating a fixed amount x of money between herself and her child wishes to give more to the child when x is larger.)

3. Infinitely Repeated Game-

Consider the following stage game repeated an infinite number of times,

Evaluate if the following strategy is a SPNE "Play (T, T). If somebody deviates play (M, M). If somebody deviates again, play (B, B)".