The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is N̄ such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with N̄ or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically. ∗ We thank seminar participants at the University of Chicago, Rutgers, Northwestern, and Washington Universities, and participants at the Murat Sertel memorial conference. The second author is grateful for the support of the Technion Fund for Promotion of Research. † Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston IL 60208. ‡ Davidson Faculty of Industrial Engineering and Management,Technion, Haifa 32000, Israel. . The Technion VPR Fund and the William Davidson Fund are gratefully acknowledged. Efficiency of Competitive Mechanisms 1