Cooperation and market socialism: Kant versus Nash

The idea that socialism depends upon cooperation, as capitalism depends on competition, has always been inherent in the conception of socialism. Yet precise models of market socialism - ones, that is, that are sufficiently articulated so as to be able to discuss and compute an equilibrium in the economy - do not model cooperation in production, or more generally, in economic behavior. We introduce a Kantian optimization protocol, which, in contrast to Nash optimization, models how individuals can cooperate in labor and/or investment decisions. We prove that the `cooperative equilibrium', thus modeled, is Pareto efficient whenever, in addition to receiving wages and rents, profits are distributed not to shareholders, but to workers and investors in proportion to their contributions to the firm. Pareto efficiency is achieved when the firms entire output is distributed to factor owners and shareholders do not exist.