The Model and Some Basic Properties

Abstract

In Part II we studied markets where some agents (the households) had imperfect information about the actions of some other agents (the prices and/or quality offers of different firms). These actions were endogenous variables of the system, and we sought to determine their equilibrium values as a function of the prevailing information structure. In other words, in Part II we were concerned with market uncertainty. Now, in Part III, we turn to the case of event uncertainty, i.e. uncertainty about variables which are exogenous for the model under consideration. Imperfect information will be essentially due to the fact that the future is uncertain. Uncertainty about the future has been formally incorporated in the standard model of general equilibrium theory (cf. Debreu ’59 Chapter 7), and it is well known that a Pareto-optimal allocation can be achieved if “state-contingent” contracts for all commodities exist (or even if they exist only for a sufficiently rich class, cf. Arrow ’53). Such a market system is called complete in the Arrow-Debreu sense or Arrow-Debreu complete for short. A state-contingent contract stipulates the delivery of a good at some future date, provided a certain “state of nature” occurs (and no delivery otherwise). Using such contracts, the agents are able to formulate, already at the initial date, trade plans that take into account all possible future developments in an optimal way.