Implementation of the Walrasian Correspondence without Continuous, Convex, and Ordered Preferences

This paper consideres the problem of designing better mechanisms whose Nash allocations coincide with constrained Walrasian allocations for non-neoclassical economies under the minimal possible assumptions. We show that no assumprions on preferences are needed for feasible and continuous implementation of the constrained Walraisan correspondence. Further, under the monotonicity assumption, we present a mechanism that is completely feasible and continuous. Hence, no continuity and convexity assumptions on preferences are required, and preferences may be nontotal or nontransitive. Thus, this paper gives a somewhat positive answer to the question raised in the literature by showing that, even for non-neoclassical economies, there are incentive-compatible, privacy preserving, and well-behaved mechanisms which yield Pareto-efficient and individually rational allocations at Nash equilibria.