Alice and Bob have the same laptop. Unfortunately, both computers have been

stolen. The insurance company wants to reimburse them at the right price and

proposes the following rule. Alice and Bob must each announce the estimated value

of their computer. The choices are made simultaneously. Let x be the value

announced by Alice and y the value announced by Bob.

-If x=y then each receives this sum

-If x

- If x>y then Alice receives y-2 and Bob receives y+2

It is assumed that the values announced must be chosen from integers between 2

and 6.

1. Write the matrix for this game

2. Show that (2,2) is the only pure Nash equilibrium.

3. We now assume that Alice plays before Bob: Alice chooses x, announces it to Bob,

who then chooses y. Solve this game by backward induction (Hint: as Alice plays

before Bob, she anticipates Bob's best answers to each of these choices).