Asymptotically Optimal Market Mechanisms

Because rational agents use their private information strategically in many trading environments any budget balanced, incentive compatible, and individually rational market mechanism will be ine¢cient. This paper is concerned with the emerging ine¢ciencies as the number of traders becomes large. We prove that the absolute ine¢ciency of a sequence of budget balanced market mechanisms can not converge to zero faster then co m , where m is the size of the market and co is a number explicitly determined in the paper. We propose a simple modi...cation of the Vickrey-Clarke-Groves mechanism which is budget balanced, individually rational, implementable in dominant strategies, and asymptotically optimal in the sense that it achieves the above rate of convergence. As a side product of our analysis we get other asymptotic results describing the trade o¤ between revenue and e¢ciency. For example, we prove that, as the market size m goes to in...nity, the minimal de...cit needed to implement the e¢cient allocation rule converges to a number do, which is also explicitly determined in the paper.