One day you lose your wallet. In it, you had 500 and some valuables that others cannot use, such as a few old photos. It will cost you another 500 to get new copies of the photos and replace the other valuables. Consequently, the wallet is worth 1,000 to you.

Fortunately, someone finds your wallet. She opens it and sees that it contains 500. She thinks that if she keeps the money and throws the wallet away, she will get 500. However, if she returns it to you she might get a reward. After all, it is worth 1,000 to you. Suppose you give her either 600 in reward or nothing.

We can represent this game as in Figure E.7.2.

a) What is the name of the method used to find the subgame perfect equilibrium?

b) Which is the subgame perfect equilibrium in Figure E.7.2?

c) Is the equilibrium efficient or not? Why or why not?

d) Can you think of a way to change the structure of the game, such that a better equilibrium will arise?