Consider the sale model (in which the seller makes all the offers). Suppose that the buyer has…

Consider the sale model (in which the seller makes all the offers). Suppose that the buyer has cost ε > 0 of starting to bargain, which must be paid before the seller makes the first offer. Show that in a perfect Bayesian equilibrium bargaining never takes place, i.e., no buyer pays the entry fee. (Hint: Consider the lowest type who enters the bargaining process.) Is this conclusion robust to the extensive form? (Hint: Suppose that the buyer makes an offer every other period, and take ε to 0.)