Suppose that Bill (a buyer) and Kandi (a seller) are bargaining over the price at which Kandi will perform a service for Bill. It is common knowledge that the maximum price Bill will pay is $300 and the minimum price Kandi will accept is $200. They bargain over the price in the following manner: Bill offers a price to Kandi, who can either accept or reject it. If she accepts Bills first offer, the game ends and they exchange at this price, P₁. Bills payoff is $300 - P₁ and Kandis payoff is P₁ - $200. If Kandi rejects the offer, then Bill offers another price, P₂, which Kandi can accept or reject, and so on. Both players discount future income by 50% per period (say this is the probability that the police arrive and interrupt their transaction). So, if Kandi accepts Bills Nth offer, P_N, then Bills payoff is ($300 P_N)/2^N-1 and Kandis payoff is (P_N - $200)/2^N-1. Kandi will accept an offer if she is indifferent between accepting and rejecting it.

1. Draw the game tree for this bargaining game under the simplifying assumption that Bills only possible offers are $200, $250, or $300 and that they bargain for only 2 rounds. That is, if Kandi rejects Bills second offer, then they do not trade and each receives a payoff of $0. Use backward induction to determine the equilibrium strategies.
2. Use backward induction to determine the equilibrium strategies for both players if the game ends after two rounds and Bill can offer Kandi anything (that is any, real positive number).
3. Use backward induction to determine the equilibrium strategies for both players if the game ends after 400 rounds and Bill can offer Kandi anything (any real, positive number).