Journal article: Endogenous sharing rules were introduced by Simon and Zame [16] to model payoff indeterminacy in discontinuous games. They prove the existence in every compact strategic game of a mixed Nash equilibrium and an associated sharing rule. We extend their result to economies with externalities [1] where, by definition, players are restricted to pure strategies. We also provide a new interpretation of payoff indeterminacy in Simon and Zame's model in terms of preference incompleteness.