The Transition from Bargaining to a Competitive Market - Williams, Steven R. (American Economic Review, 2016)
How few traders constitute a bargaining problem or, alternatively how many traders constitute a market? Intuitively, people who meet to trade face a bargaining problem if several of them, with opposing interests, can influence the outcome of trade through their behavior. Traders constitute a competitive market only if the effect of any trader on the outcome of trade is insignificant. Analysis of bargaining using noncooperative game theory has been a lively research topic over the past ten years, while the formalization of perfectly competitive markets using a continuum of traders is now several decades old. In this paper I discuss a line of research that studies the transition between these two theories; in particular, a result from Mark Satterthwaite's and my paper (1989b) is presented that shows how a bargaining problem is transformed into a market as the number of traders increases. Incomplete information is an essential feature of the model that I discuss. In order to explain how traders achieve a competitive equilibrium, it is standard to assume that all potential gains from trade are commonly known at the outset. In contrast, each trader in the model that I describe privately knows his own preferences. A second feature is that a market with any finite number of traders on each side is modeled, rather than one with a continuum of traders. These two features together make strategic behavior seem especially likely. Price-taking behavior is not an axiom here; instead, the objective is to prove that a trader's equilibrium behavior is to increasingly act as a price taker as a market grows in size, and that only a small number of traders is needed on each side to compel each trader to act in this way. Though the background of this research will be discussed later in more detail, it is basically motivated by the intuition most of us share that a market can work pretty well despite having a relatively small number of traders who strategically act on their private information. While the axioms of perfect competition are, of course, never satisfied in the real world, I believe that this theory provides insight not only into immense markets but also into smaller markets. The research that I describe is another attempt to substantiate this belief.