Information Aggregation, Strategic Behavior, and Efficiency

Consider a Cournot market with n consumers and n firms facing increasing marginal costs of production subject to independent shocks which are private information to the firms. There are two sources of inefficiency present: Market power and private information. We show that the wedge between the Bayesian Cournot equilibrium (BCE) and first best efficiency (full information and price taking) is of the order of "one over radical n" for prices and l/n for (per capita) expected total surplus (ETS). This means that the Cournot market, in contrast to some auction mechanisms, is not well approximated by the standard competitive model for moderate n. Furthermore, the culprit is the lack of information aggregation and not market power. Indeed, the deviation of the Bayesian price-taking equilibrium price from the full information competitive price is of the order of "one over radical n," yielding a discrepancy in terms of (per capita) ETS of the order of 1/n. Meanwhile, the discrepancy between market prices at the BCE and at the Bayesian price-taking equilibrium is of the order of l/n and the corresponding (per capita) ETS difference is of the order of 1/n squared. This latter result generalizes to information structures with common value elements where convergence of the BCE to the full information competitive equilibrium as n grows need not obtain (however, the Bayesian price-taking equilibrium is efficient restricting attention to decentralized strategies).