Economics Letters 40 (1992) 299-302 North-Holland 299 Incentive compatibility and competitive allocations Matthew 0. Jackson * Northwestern Unicersity, Evanston IL, USA Received 31 August 1992 Accepted 29 September 1992 It is shown that as the number of individuals in an economy grows, the demand functions which are optimal for an agent converge to the competitive (price-taking) demand. 1. Introduction In the classical economic paradigm, individuals are price takers. The competitive assumption is that agents cannot affect the price and so have no strategic considerations in deciding on the quantities which they wish to buy or sell at given prices. In a seminal paper, Hurwicz (1972) showed that strategic considerations are substantial in small markets. He showed that agents may have strong incentives to choose demands which are quite different from their competitive ones in order to influence the price. In order to justify the competitive assumption it is thus necessary to limit attention to large economies. Although the intuition behind this justification is straightforward, the details of showing that competitive behavior is a reasonable approximation in large economies are somewhat touchy. In reality, economies (however large) are finite. So, to justify the competitive assumption one needs to show that behavior converges to competitive behaviour, as the size of the economy grows. In this spirit, Roberts and Postlewaite (1976) examine sequences of economies which are growing in the number of individuals and which converge to a well-behaved limiting distribution of types. They show that in such a sequence, choosing the competitive demand is limiting individually incentive compatible. (Given any E, there is a large enough economy so that the utility to an individual associated with an alternative demand is no more than E above the utility associated with the competitive demand.) Their result shows that for large economies, there is little incentive to any individual to deviate from purely competitive behavior. The Roberts and Postlewaite result, however, does not rule out deviations. It only indicates that the gains from such deviations are shrinking. Although the gains from deviations are small, they still exist. Thus we still do not know if the actual behavior of a rational agent will converge to the Correspondence to: Matthew Jackson, Kellogg Graduate School of Management, Northwestern University, Evanston, IL 60208-2009, USA. * I am grateful to Alejandro Manelli for helpful conversations. 0165.1765/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved