Journal Article Choosing an Investment Program among Interdependent Projects Get access Stanley Reiter Stanley Reiter Lafayette, Indiana Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 30, Issue 1, February 1963, Pages 32–36, https://doi.org/10.2307/2296028 Published: 01 February 1963

This paper is concerned with the amount of communication that must be provided to implement a performance standard by a mechanism whose stationary messages have the Nash property. In p articular, the authors study implementation of Walrasian allocations in exchange environments. They show that the smallest message space t hat implements Walrasian allo-cations is one of dimension, roughly, n E (. 1 1)& ./(n 1 1), where . is the number of commodities and n the number of agents. The authors exhibit an implementing mechanism whos e message space has that dimension. Copyright 1988 by The Econometric Society.

[In recent studies of economic organization [9 and 15] it has been found necessary to impose certain restrictions (regularity conditions) on the communication process. Such restrictions limit the class of environments for which the organization is Pareto satisfactory. We show that a class of environments admits a Pareto satisfactory (and regular) resource allocation mechanism if and only if the graph of the Pareto correspondence is a union of continuous functions. We also study the shape of the Pareto set for a given environment and the way that set varies as the environment varies. We present examples showing that near any environment whose Pareto utility frontier is homeomorphic to a simplex there is whose Pareto frontier is badly chopped up. We also give an example of a class of environments for which the Pareto correspondence has no continuous selection through a given point.]

[This is the second part of a paper concerning an iterative decentralized1 process designed to allocate resources optimally in decomposable environments that are possibly characterized by indivisibilities and other non convexities. Important steps of the process involve randomization. In Part I we presented the basic models and results, together with examples showing that certain assumptions can be satisfied in both classical and non convex cases. Part II goes further with such examples in showing that our process yields optimal allocations in environments in which the competitive mechanism fails, and also shows how abstract conditions used in Part I can be verified in terms of properties of preferences and production functions that are familiar to economists.]