- This paper deals with the problem of incentive mechanism design in non-convex production economies when production sets and preferences both are unknown to the designer. We consider Nash-implementation of loss-free, average cost, marginal cost, voluntary trading, and quantity-taking pricing equilibrium allocations in economies involving increasing returns to scale or more general types of non-convexities. The mechanisms presented in the paper are well-behaved. They are feasible, continuous, and use finite dimensional message spaces. Moreover, the mechanisms work not only for three or more agents, but also for two-agent economies. 2008 Elsevier Inc. All rights reserved.