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General equilibrium with private state verification

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Abstract

We study general equilibrium with private and incomplete state verification. Trade is agreed ex ante, that is, before private information is received. It is useful to define a list of bundles as a derivative good that gives an agent the right to receive one of the bundles in the list. Enforceable trade agreements can be described by Pi-measurable plans of lists of bundles, instead of Pi-measurable plans of bundles as in Radner (1968). In equilibrium, the price of a list coincides with the price of the cheapest bundle in the list, and it is always the cheapest bundle of the list that is delivered. This property leads to a system of linear inequalities which are deliverability constraints on the choice set. We investigate existence of equilibrium in the case in which preferences are Pi-measurable. If there is a perfectly informed trader in the economy, existence of equilibrium is guaranteed.

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