Convergence to Efficiency in a Simple Market with Incomplete Information
Mark A. Satterthwaite
Steven R. Williams
A model of trade with $m$ buyers and $m$ sellers is considered in which price is set to equate revealed demand and supply. In a Bayesian Nash equilibrium, each trader acts not as a price-taker, but instead misrepresents his true demand/supply to influence price in his favor. This causes inefficiency. We show that in any equilibrium the amount by which a trader misreports is $O(1/m)$ and the corresponding inefficiency is $O(1/m^2)$. The indeterminacy and the inefficiency that is caused by the traders' bargaining behavior in small markets thus rapidly vanishes as the market increases in size.