Bargaining with Arrival of New Traders

In bargaining theory (and practice), outside options play an important role. Often, an important outside option is to wait for new developments. Maybe another agent will show up and offer better terms of trade, maybe new information will arrive reducing the information asymmetry, etc. Traders compare these potential benefits to costs of delaying trade and the risk that over time the opportunity to trade might disappear (or that unfavorable information will arrive, etc.). In this paper we study a general bargaining model that captures outside options of this nature and characterizes their impact on the dynamics of bargaining. For example, suppose you have put your house on the market. So far only one buyer has expressed interest. He informs you that your original price is too high and asks you to reduce it. What do you consider before responding? Out of many factors that you may take into account, two important ones are: 1) How likely it is that other serious buyers will show up in the short run? 2) How likely it is that if you wait to reduce the price, the current buyer will find another house and “disappear”? In fact, these risks in many situations are likely to be more important in evaluating the relative costs and benefits of delay than the standard discounting costs that play a crucial role in many bargaining models. This intuition is confirmed by our model. New traders arriving over time is a common feature of many markets (housing, labor, financial markets to name a few). A key characteristic of such markets is that trade/bargaining over price takes time, and the bargaining dynamics are heavily influenced by the market conditions. For example, the asking price of a house takes time to drop, and how long it takes may depend on whether it is a “sellers’ market” or a “buyers’ market.” We shed some light on how such external conditions affect the dynamics of bargaining. We start with an abstract, general bargaining game: there is a buyer and a seller. The seller has an asset that he values at zero (normalization). The buyer has private information about his value, Bargaining with Arrival of New Traders