Decision Making Under Risk and Uncertainty
As desired, the infonnation demand correspondence is single valued at equilibrium prices. Hence no planner is needed to assign infonnation allocations to individuals. Proposition 4. For any given infonnation price system p E. P (F *), almost every a E A demands a unique combined infonnation structure (although traders may be indifferent among partial infonnation sales from different information allocations, etc. ). In particular, the aggregate excess demand correspondence for net combined infonnation trades is a continuous function. Proof Uniqueness fails only if an agent can obtain the same expected utility from two or more net combined infonnation allocations. If this happens, appropriate slight perturbations of personal probability vectors destroy the equality unless the utility functions and wealth allocations were independent across states. Yet, when utilities and wealths don't depend on states in S, no infonnation to distinguish the states is desired, so that the demand for such infonnation structures must equal zero. To show the second claim, recall that if the correspondence is single valued for almost every agent, then its integral is also single valued. Finally, note that an upper hemicontinuous (by Proposition 2) correspondence which is single valued everywhere is, in fact, a continuous function.  REFERENCES Allen, Beth (1986a). "The Demand for (Differentiated) Infonnation"; Review of Economic Studies. 53. (311-323). Allen, Beth (1986b). "General Equilibrium with Infonnation Sales"; Theory and Decision. 21. (1-33). Allen, Beth (1990). "Infonnation as an Economic Commodity"; American Economic Review. 80. (268-273).