Adrian (player A) and Bani (player B) are in a restaurant. The owner offers S slices...

 

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Adrian (player A) and Bani (player B) are in a restaurant. The owner offers S 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: S/2 2,S/2,S/2+2, and S. Let SA and SB respectively denote the numbers announced by A and B. If SA + SBS, then each gets what they announce. Otherwise, if SA + SB > S, each gets 0. We assume that player i's utility equals the number of slices player i gets. Both A and B maximize their own utility. Assume S = 10. (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 (SA, S-SA) to B where, as before, SA can take one of the four values: S/2-2, S/2, S/2+2, S. If B accepts the split, then A gets s A and B gets S-SA. 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 SA Adrian (player A) and Bani (player B) are in a restaurant. The owner offers S 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: S/2 2,S/2,S/2+2, and S. Let SA and SB respectively denote the numbers announced by A and B. If SA + SBS, then each gets what they announce. Otherwise, if SA + SB > S, each gets 0. We assume that player i's utility equals the number of slices player i gets. Both A and B maximize their own utility. Assume S = 10. (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 (SA, S-SA) to B where, as before, SA can take one of the four values: S/2-2, S/2, S/2+2, S. If B accepts the split, then A gets s A and B gets S-SA. 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 SA