Game theory is both at the heart of economics and without a definitive solution. This paper proposes a solution. It is argued that a dominance criterion generates a, and perhaps the, generalized equilibrium solution for game theory. First we provide a set theoretic perspective from which to view game theory, and then present and discuss the proposed solution.
General competitive analysis is extended to cover a dynamic, pure-exchange economy with privately observed shocks to preferences. In the linear, infinite-dimensional space containing lotteries we establish the existence of optima, the existence of competitive equilibria, and that every competitive equilibrium is an optimum. An example illustrates that rationing and securities with contrived risk have an equilibrium interpretation.