POSTED PRICES VERSUS BARGAINING IN MARKETS WITH ASYMMETRIC INFORMATION

I. INTRODUCTION The spirited bargaining of the bazaar has been the predominant price setting mechanism in most producer and consumer markets in the Western world for many centuries whereas the use of posted prices to optimize profits is a relatively recent phenomenon.(1) The ascent and eventual widespread use of posted prices began in 1823(2) when Alexander Stewart introduced posted prices in his New York dry goods store - the forerunner of his famed Marble Dry Goods Palace.(3) Originally considered a gimmick, the advent of this revolution in retail pricing became evident as his store grew to become the largest in the U.S. and other famous merchants followed his lead.(4) Currently, both bargaining and posted prices are common means of establishing trading prices. The purpose of this paper is to provide a model of pricing institutions, consistent with the fact that some markets witness posted prices while others witness bargaining, in order to predict when each of these mechanisms will be utilized. Our modeling begins with a single seller who, sequentially encountering potential buyers, seeks to sell a good by using one of two pricing mechanisms - a posted price or bargaining - and a population of consumers who are distinguished by two characteristics: each buyer has a private value v for the good and a bargaining ability [Gamma]. A buyer's bargaining ability reflects the proportion of the gains from trade he captures when bargaining with the seller. These characteristics are distributed independently across the population of consumers according to random variables V and [Gamma]. Search costs, discount factors, and the distributions of V and [Gamma] are all common knowledge. Our assumption that bargaining ability differs across buyers is easily motivated. One explanation emanates from buyers possessing different discount factors. Then, by Rubinstein's [1982] result, more patient buyers exhibit better bargaining ability and acquire a larger share of the gains from trade. An alternative and compelling source of bargaining ability is provided by Diamond [1987, 279] who speaks of the reality of actual markets in which "infrequent traders are often ill-informed ... [thereby creating an incentive for] sellers to find consumers whose beliefs make them willing to trade at high prices." Similarly, Stigler [1961, 218-19] notes the "widely held view that inexperienced buyers (tourists) pay higher prices than do experienced buyers." The relevance of buyer information and experience to the seller's choice of a selling mechanism is underscored by Macy's advertisements from the 1850s, which stated that prior to the use of posted prices (by Macy's), "there was no regular price for anything and the most ignorant were the most imposed upon," while with posted prices "a child can trade with us as cheap as the shrewdest buyer in the country" (Scull [1967, 83]).(5) Other sources of differential bargaining ability include differences in the opportunity cost of failing to reach an agreement, the existence of outside opportunities, risk-aversion, willpower, and the buyer's intrinsic poker face or ability to conceal the maximum amount he is willing to pay. As we shall see, the observability or non-observability of the buyer's characteristics v and [Gamma] is not important. In addition, the source of the buyer's bargaining ability [Gamma] is not important. What is important is that (a) buyers differ from one another, (b) there is some reasonable way of determining whether or not trade occurs and how the gains from trade are divided between the seller and a buyer with a given characteristic pair, and (c) the bargaining process differs with different buyers. In particular, when bargaining with a weak buyer, the seller acquires a greater portion of the gains from trade than when bargaining with a strong buyer.(6) In our model buyers willing to trade at high prices are characterized by a high private value v and a low bargaining ability [Gamma]. …