The determination of the mechanism for ordering strategies in a game theoretic conflict is the keystone of economic science, at least insofar as economics is to remain an outgrowth of that (otherwise relatively minor) school of English philosophy, Utilitarianism. A method for the solution of the general game is presented in this paper, and the implications for economic theorizing discussed.

We analyze economies with indivisible commodities. There are two reasons for doing so. First, we extend and provide new insights into sunspot equilibrium theory. Finite competitive economies with perfect markets and convex consumption sets do not allow sunspot equilibria; these same economies with nonconvex consumption sets do, and they have several properties that can never arise in convex environments. Second, we provide a reinterpretation of the employment lotteries used in contract theory and in macroeconomic models with indivisible labor. We show how socially optimal employment lotteries can be decentralized as competitive equilibria once sunspots are introduced.