Question

A proposer (P) and a respondent (R) need to divide $100. The proposer offers to keep x dollars and to give 100?x dollars to the respondent. If the respondent accepts, they distribute the money accordingly. If the respondent rejects, each get zero. We will assume that any value x ? [0, 100] is a valid offer.

(a) Find the SPNE payoffs in this game.

Answer 1

Solving the game by backward induction, the respondent will accept any offer that he gets an amount greater than 0 because if he rejects an offer, he gets 0. The proposer knows this and has the first mover advantage. The proposer maximizes his payoff and offers to keep 100-e (where e is a very small amount greater than 0). The respondent gets an amount of e in the equilibrium. The respondant's optimum stratergy is to accept any offer greater than 0 and the proposer's strategy is to offer any amount greater than 0.