Information precision and asymptotic efficiency of industrial markets

I present a strategic model of a bilateral oligopoly with asymmetric information to examine (i) the validity of the conjecture of price-taking behavior in such markets as the number of agents becomes large and (ii) the effect of the rate that individual information precision decreases with increased number of agents on convergence to price-taking and efficiency. I show that with downstream competition, increasing the number of sellers may make all participants price-takers in the limit, but increasing the number of buyers may not. When the total precision of information in the market is high, price-taking and full social efficiency is achieved in the limit with large numbers of buyers and sellers. However, if the total precision of information in the market is poor, price-taking conjecture may fail and large inefficiencies, including full inefficiency, can occur in the limiting outcome. The rate of decrease of individual information precision with increased number of agents determines the rate of convergence to efficiency, and the convergence is slower than that predicted by single-unit auction models in the literature. I also demonstrate that when the number of sellers or both the number of buyers and the sellers go to infinity, price-taking and information aggregation tend to go together. When the number of buyers goes to infinity, however, information can get aggregated when the agents do not become price-takers in the limit. Albeit, in the latter case, the aggregated information is masked by the noise in the sellers' signals and the cost variability.