Noncooperative price taking in large dynamic markets
This chapter discusses noncooperative price taking in large dynamic markets. Cournot's proposition that large markets are competitive is reconciled with the possibility of equilibrium involving strategic interaction among firms. It is shown that, except when extraordinarily precise information is available, firms in a market with many agents are not visible enough for the equilibrium described by Stigler to be sustained. This result is proved by studying two formal representations of markets with many agents. One of these representations involves initially choosing a particular market, with finitely many participants, and then forming a sequence of increasingly large markets by adjoining at each stage a new copy of the original one. The result of this procedure is called a sequence of replica markets. All of the markets in the sequence have the same statistical characteristics, the ratio of firms to consumers is constant, and they all share the same competitive market-clearing prices. The other representation of markets with many agents exploits the fact that, if counting measure on the set of agents in a market is normalized to make the set into a probability space, then a description of agents' characteristics and actions is mathematically a random vector defined on the sample space of agents.