Mechanism design for an economy with increasing returns to scale

I have designed a mechanism in an economy with increasing returns to scale which satisfies the following properties: (1) Informational Decentralization. The central agent (CA) need not know the consumer's or any firm's private environments, i.e., the consumer's utility function and his initial endowment, or any firm's production function. (2) Efficiency. A locally unique stationary point is locally stable if and only if it is locally optimal.; The following informationally decentralized mechanisms have been among those proposed for increasing returns economies: marginal cost pricing (MCP) mechanisms, the average cost pricing (ACP) mechanism, and the Arrow and Hurwicz mechanism. The MCP and ACP mechanisms are informationally decentralized mechanisms, since both the designer and the CA need not know an agent's private information. However, a MCP equilibrium allocation may not even be a locally Pareto optimal allocation, since the second order necessary conditions for local Pareto optimality may be violated. The ACP mechanism also need not realize a locally optimal allocation. In contrast, the Arrow and Hurwicz mechanism satisfies local Pareto optimality. However, although the CA need not know other agents' private information, the designer must have some information about environments to determine the size of the concavification parameters. The Heal, Aoki, and Cremer mechanisms are not informationally decentralized.; Thus it is natural to ask whether or not there exists an informationally decentralized mechanism that satisfies local Pareto optimality. Calsamiglia showed that there is no informationally decentralized mechanism with a finite dimensional message space which realizes a globally optimal allocation in a rich class of environments with increasing returns. In fact, the same appears likely to hold for locally optimal allocations. A reasonable finite dimensional message space compromise is to introduce dynamics whose stationary points are locally optimal if and only if they are locally stable. This is a property of my mechanism. My mechanism uses a finite dimensional message space so it has stationary points which are not locally optimal, but these points are not locally stable, and in that sense they are not likely to be observed in reality.