First-Offer Bargains

In the well-known model of bilateral monopoly a single seller of a good faces a single potential buyer. Frequently, each party will be uncertain about the other's reservation price. Thus, in making a price offer each faces a trade-off between his individual gains (if a bargain is successful) and the probability that a mutually acceptable bargain is concluded. This paper focuses on the implications of a bargaining rule that calls for one party to make the first and final offer, the other to accept or reject it. As one would expect, the buyer offer strategy involves "shading". (quoting of an offer below his true reservation price for the good) while the seller employs a "markup" offer strategy. The offer strategy of each party is nondecreasing in the individual's reservation price. Furthermore, a uniformly more optimistic assessment of the opponent's reservation price (in the special sense of stochastic dominance) induces a less truthful offer from the individual. While the relative efficiency of the buyer and seller first-offer procedures must be examined on a case-by-case basis, it can be shown that the opportunity to make the first and final offer always confers a distinct bargaining advantage.