Question 8 (3 points) Adrian (player A) and Bani (player B) are in a restaurant. The owner offers 5 slices of pizza for free under the following condition. A and B announce the number of slices they would like. Each can announce (exactly) one of the four numbers: 8/2 2, 5/2, 3/2 l 2, and 3. Let 3A and .93 respectively denote the numbers announced by A and B. If 5A + 33 g S, then each gets what they announce. OthenNise, if 3A + .913 > S, each gets 0. We assume that player is utility equals the number of slices player i gets. Both A and B maximize their own utility. AssumeS : 6. (a) (1.5 points) Suppose A and B announce the number of slices simultaneously. In this simultaneous move game, the number of Nash equilibria in pure strategies is (b) (1.5 points) Now consider a sequential move game where A proposes a split (5A, 3* 3A) to B where, as before, 3A can take one of the four values: 3/272,S/2,S/2+2,S. ',QE&J:2 If B accepts the split, then A gets 5A and B gets 378A. Else, if B rejects, each gets 0. If indifferent between accepting and rejecting a proposal, we assume B rejects. In the unique subgame perfect equilibrium of the game A proposes 8A 2E