Are there non-dictatorial outcome functions (game forms) such that (1) for every preference profile there exists a Nash equilibrium, and (2) for every profile, every Nash equilibrium outcome is Pareto optimal? For more than two persons, if indifferences are ruled out or if only "weak" Pareto optimality is required, the answer is shown to be in the affirmative. For two persons it is in the negative. Among other questions explored are voting system interpretations and symmetry properties of outcome functions.