Question

Question 5 (20 points). Consider the following game between Kyle and Anna. The students are given $15 to split between them. Kyle makes the first move and offers Anna a portion of $15. If she accepts, the bargain is complete and the students each get an amount determined by Kyle's offer. If she declines, the $15 shrinks to $10 and Anna then gets a turn to make Kyle an offer. Again, the bargain is complete if Kyle accepts and the division is made according to the terms of Anna's offer. If he declines, the $10 shrinks to $5 and Kyle gets to make an offer. If Anna accepts, the division is made according to Kyle's offer, but if she declines, the $5 shrinks to zero and each student receive nothing. Rollback analysis enables us to predict the outcome of this alternating-offers game. If the game has gone to the point where only $5 is left, Kyle offers Anna S0. Anna accepts this offer, since rejection will not make her better off. (a) Backing up one round, answer the following question: if the game reached the point where $10 is left, what would Anna offer? (b) When Kyle makes the first move, what does he offer?

Answer 1

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