A necessary condition for realization by a decentralized finite-dimensional mechanism is proved. The concepts of the realization of a time sequence of allocations by a decentralized temporal process and by the particular more realistic class of decentralized evolutionary temporal processes are defined. The above condition shows that the optimal allocation in a simple model for intertemporal production and consumption can be realized by a decentralized temporal process but not by a decentralized evolutionary process which uses either a finite number of verification conditions or a finite-dimensional message space.
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*This work is a result of the 1983-1984 program on Mathematical Models for the Economics of Decentralized Resource Allocation at the Institute for Mathematics and its Applications. Earlier versions were presented at the IMA and at the Economics Department of the University of California at San Diego in 1984. We are grateful to the referees and the Associate Editor for numerous helpful suggestions. The first author was supported by the National Science Foundation through Grants IRI-8510042 and SES-8509547. The second author was supported by grants from the National Science Foundation and the Air Force Oftice of Scientific Research.