Question 3 [3 points] Adrian [playerA] and Bani {player B} are in a restaurant. The owner offers 3 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: SIB 2. $2.51\"? + 2. and 5. Let 3:1 and 33 respectively denote the numbers announced by A and B. If 3:1 + 33 5 .5'. then each gets what they announce. Otherwise; if 3w + 33 '::- 5'. each gets D. We assume that player is utility equals the number of slices player i gets. Both A and B maximize their own utility. Assume S = B. (a) {1.5 points] Suppose A and B announce the number of slices simultaneously. In this simultaneous move garner the number of Nash equilibria in pure strategies is [b] {1 .5 points} Now consider a sequential move game where A proposes a split [5,1, 3 5'4} to B where, as before, 5.4, can take one of the four values: 532 2+ SE. SE + 2+ 3. If E accepts the split, then A gets SA and El gets 33.1. Elser if E! rejeets, each gets CI. If indifferent between accepting and rejecting a proposal, we assume B rejects. In the unique subgame perfect equilibrium of the game A proposes 3w =