A LABORATORY STUDY OF DUOPOLY PRICE COMPETITION WITH PATIENT BUYERS

I. INTRODUCTION Two extreme forms of pricing behavior--sometimes called the Bertrand Paradox and the Diamond Paradox--emerge from a single distinguishing assumption. Bertrand (1883) assumes that a buyer knows ex ante the prices of all sellers, and notes that with homogeneous goods a single competitive price emerges even among a small number of sellers because at any slightly higher price at least one seller can increase his profit by engaging in undercutting. In Diamond's (1971) model, on the other hand, a buyer first chooses a seller and then receives the price quote ex post. Even with infinitesimal search cost, in equilibrium a buyer searches only one seller and all sellers charge the monopoly price. The only difference between the two formulations is whether sellers price ex ante or ex post. (1) Intuitively however, there is no strong rationale for preferring either assumption for when price information is acquired. This is especially so since the "law of one price" is known to fail, and persistent price dispersion is widely observed even in essentially homogenous goods markets (e.g., Baye, Morgan, and Scholten 2004; Brynjolfsson and Smith 2000; Sorensen 2000). Most of the theoretical literature that models price dispersion has employed costly buyer search (e.g., Salop and Stiglitz 1977, 1982; Stahl 1989, 1996; Stigler 1961) or costly seller advertising (Butters 1977; Robert and Stahl 1993) to generate dispersed prices. (2) Gale (1988), on the other hand, models price dispersion in a rather stark form, using only two sellers and one buyer. This can provide a modeling foundation for some types of multilateral bargaining such as in concentrated intermediate goods markets. Sellers are uncertain whether the buyer is receiving price offers from both (ex ante pricing) or one (ex post pricing) of them at any given time. If the buyer's sample contains both offers with a positive but not certain probability [gamma], a unique dispersed price equilibrium exists that shifts systematically with [gamma]. Extending this static model to multiround pricing with time discounting, Gale examines the impact of greater buyer patience--modeled as a higher discount factor--on the equilibrium price level and price dispersion. This is intended to approximate market conditions with many buyers where trade continues over time, as can occur also in durable goods settings. As buyers become more patient, sellers must compete not only with the other seller but also with their own future price offers; consequently, the equilibrium price distribution becomes concentrated at lower prices. This article presents the first laboratory experiment that studies the interaction of buyer patience and search with multiround pricing by competing sellers. Specifically, we focus on prices posted by competing sellers in a noisy search environment where buyers can wait for more price offers. This enables us to explore how the timing of buyer's purchase decisions influences sellers' pricing strategy, which is not captured by the stationary equilibrium of the theoretical model. The experiment includes both a static treatment, where agents have only one opportunity to trade each period, and a dynamic treatment where trading opportunities may continue for future rounds of price offers with a positive and known probability, 3. One interpretation of these single-round trading and multiple-round trading treatments is that the former refers to a disposable goods and the latter to a durable goods environment. The model's predictions that prices decrease if the buyer is more patient or is more likely to receive both price offers are intuitive, but the available evidence from previous durable goods and bargaining experiments provides only weak support for theory. Furthermore, implications of multiple price offers from competing sellers have never been studied previously in experiments with durable goods and multiple-round trading, which have focused on single seller environments. …