Be sure to label who plays at each decision node, what action each branch represents, and the payoffs at each terminal node. For each strategy profile, state whether or not the profile is a Nash Equilibrium. For those strategy profiles that are not Nash Equilibria, explain why they are not. Using backward induction, find the solution to this game. Suppose Bill, a buyer, and Sally, a seller, are bargaining over the price at which they make a trade.
Bill plays first.
Sally may accept, in which case the game ends, or she may reject and then make a counter offer in the next period. Bill may accept or reject the counter offer, at which point the game ends. Bill and Sally both discount future gains from trade at the same rate. A player who is indifferent between accepting and rejecting will always accept. Be sure to label who plays at each decision node, what action each branch represents, and the payoffs at each terminal node.