game theory

l. (30 Points) Consider the ultimatum-offer bargaining game that we discussed in lectures: The buyer makes an offer 3 E [0,100]. The seller observes this offer and then either accepts or rejects it. If she rejects, then both players get i} payoff. If she accepts the offer, then the buyer's payoff is 100 - b and the seller's payoff is b. (a) (10 Points) Is there a Nash equilibrium where the seller accepts any offer 6 \".1:- D but rejects b a [1? Carefully explain your answer. (b) (10 Points] Find the Subgame Perfect Nash equilibrium outcome(s) and strat- egy prole(s) of this game. (c) (10 Points) Prove or disprove: For any h E [l], IUD], there is a Nash equilibrium of this game in which an agreement is reached at this price