Efficient Sequential Bargaining

Abstract

Suppose that a seller and a buyer have private valuations for a good, and that their respective utilities from a trading mechanism are given by u s and u b . (These utilities are determined by the valuation for the good, by whether a trade occurs, and by the price which is paid.) Consider the problem of maximizing E[λ u s + (1 − λ) u b ] for some weight λ in the unit interval. It is shown in this article that, if λ is sufficiently close to zero or one, then the maximum value of this objective function attainable by a static revelation mechanism can be arbitrarily closely approximated by equilibria of the sequential bargaining games in which only a single player makes offers. That is, the welfare bound implied by the revelation principle is virtually attainable in offer/counteroffer bargaining. The main condition needed for this result is a monotone-hazard-rate assumption about the distribution of types. A class of examples is presented in which the result holds for all λ (i.e. the entire ex ante Pareto frontier).