Name Key

Harry has a car for sale. It may be either good  or bad. If it is a bad car then he can spiff it up by spending $10 on it.  Cleaning and polishing it does not change the car's quality, it just makes it look like a good car.  Edith wants to buy a car.  The value of a good car to Edith is $100.  The value of a bad car to Edith is $75.  Edith believes that there is an 80% probability that Harry's car is good.  If Harry offers to sell the car then his asking price will be $90. The game tree looks like:

1.  If Edith agrees to buy any car offered to her, what is her expected payoff? 5

2.  If Edith is willing to buy any car offered to her, what is Harry's dominant strategy? Sell(good), Sell(bad)

3.  If Edith is willing to buy any car offered, how high would cleaning and polishing costs have to be before Harry had an incentive to withhold a 'bad' car from the market? 90

4. For your own use, write out the strategic form of the game.  What is the IEDS solution to the game between Edith and Harry?

Harry's plan  Sell(good), Sell(bad)  Edith's plan Buy

5. Using your strategic form of the game, is there another Nash Equilibrium?  Yes    No Edith plays Refuse and Harry plays Withhold(g), Withhold(b).

6.  Given the Harry's costs of cleaning and Edith's dominant strategy, is the solution to this model a pooling or a separating equilibrium? This is a pooling equilibrium since both types of cars are made available at the same price.

7.  Is this market result efficient, i.e., all market participants regard the deal they have made as a good one? Yes  No To be efficient the equilibrium must be a separating equilibrium.

Let's change things a bit. The value of a good car to Edith is still $100; the value to her of a bad car is still $75. She still believes that 80% of cars offered for sale are of good quality.  The cost of cosmetic repairs, cleaning and polishing has risen to $90 and the price of a car in the market place is now $80.  The new game tree is

8.  If Edith agrees to buy any car offered to her, what is her expected payoff? 15

9.  Given her expected payoff from buying any car, what strategy should Edith use at her information set encompassing nodes G & B? Buy

10.  What is Harry's payoff when Edith buys a 'bad' car from him? -10

11.  Will Harry offer a bad car to Edith? Yes  No

12. For your own use, write out the strategic form of the game.  What is the IEDS solution to the game?

Harry's plan    Sg, Wb Edith's plan  Buy

13.  Is there another Nash Equilibirum? Yes  No  , if so, what is it Edith Refuses and Harry plays Wg, Wb

Harry's plan   Edith's plan

14.  Is the solution to this game a pooling or a separating equilibrium?

15. Is this market result efficient, i.e., all market participants regard the deal they have made as a good one? Yes  No

Let's return to the original data.  Harry can spiff up the car at a cost of $10.  Edith values a good car at $100 and a bad car at $75.  The price of the car when a sale takes place is $90.  One thing has changed: Edith now believes that only 20% of the cars offered by Harry are of good quality.  The game tree is pictured below:

16.  If Edith agrees to buy any car offered to her what is her expected payoff? -10

17.  Given her expected payoff from buying any car offered to her, what should be Edith's strategy at the nodes G & B in her information set? Refuse

For your own use, write out the strategic form of the game.

18.  Given Edith's strategy, what strategy should Harry employ? Edith Refuse, Harry Wg, Wb

19.  Is this equilibrium a separating or a pooling equilibrium?

20. Is the market corresponding to this equilibrium efficient? Yes  No