Convergence to Price-Taking Behavior in a Simple Market
An independent private values model of trade with m buyers and m sellers is considered in which price is chosen to equate revealed demand and supply. In ever symmetric Bayesian Nash equilibrium, each trader does not act as a price-taker, but instead strategically misrepresents his true demand/supply to influence price in his favor. This misrepresentation causes inefficiency. It is shown that the amount by which a trader misreports is 0(1/m) and the corresponding influence is 0(1/m^2). Price-taking behavior and its associated efficiency thus quickly emerges despite the asymmetric information and the noncooperative behavior of traders.
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