7. Alice and Bob can play either of these two games: The Red Game The Green Game

Question

7. Alice and Bob can play either of these two games: The Red Game The Green Game Alice Alice Left Right Left Right Alice gets 2 Bob gets 5 Alice gets 0 Bob gets O Alice gets 5 Up Bob gets 2 Up Alice gets 4 Bob gets 3 Bob Bob Alice gets 2 Alice gets 5 Bob gets i2 Alice gets 0 DownBob gets 5 DownBob gets 0 Alice gets 3 Bob gets 4 One of the players is called the Chooser and the other is called the Decider. The Chooser decides which of the two games they will play. Then the Decider decides which of the two players will go first Would Alice prefer to be the Chooser or the Decider?

Explanation / Answer

There are two games here and the pure strategy Nash equilibriums in these games can be given by (Up, Left) and (Down,right) in the second game with payoffs of (3, 4) and (4, 3). These payoffs are received with surety. In the first game there are no pure strategy Nash equilibria. There is an equilibrium in mixed strategies given by where Bob plays up with probability 2/7 and he plays down with probability 5/7. Thus in this case Alice would prefer to be the Chooser and she will choose the second game where she gets the payoffs with surety rather than with a probability as in the case.

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