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Unformatted text preview: Problem Set 6 Due Thursday, Dec. 3rd, by 10pm 1. Consider a game where a buyer makes a take it or leave it offer, p, to a seller who then decides whether to accept the offer. (a) Suppose the buyer's payoff is 5-p if the offer is accepted and 0 if the offer is not accepted. The seller's payoff is p if the offer is accepted and 1 if the offer is not accepted. Find a subgame perfect Nash equilibrium and and a Nash equilibrium that is not subgame perfect. (b) Suppose now that the seller can make an investment which is observed by the buyer before the buyer makes an offer. If the seller makes the investment, this improves the payoff for the buyer if the offer is accepted to 8 - p but lowers the payoff of the seller to p - 1 if the offer is accepted and 0 if the offer is not accepted. What is a subgame perfect Nash equilibrium to this game? (c) Now suppose the game was repeated forever. Find a trigger strategy and the values of which support a SPNE outcome of the seller investing, the buyer setting p = 3, and the seller accepting the offer in every period. 2. Consider the signaling game on the next page. A signaling game involves nature determining the payoffs for both players. The first player moving based upon this information. The second player only sees the first player's move and knows the payoffs conditional on every move/nature combination. (a) A pooling equilibrium is a Perfect Bayesian equilibrium where, regardless of nature's move, the first player always makes the same choice. Find a pooling equilibrium to the game. (b) A separating equilibrium is a Perfect Bayesian equilibrium where the first player makes a different move depending upon what nature does. Find a separating equilibrium to the game. 1 ...
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This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.
- Fall '09