Allocation of resources in a team

The informational efficiency of “price” and “demand” messages in a resource allocation mechanism is studied here with the aid of the theory of teams¹. In the usual analysis of adjustment mechanisms (tâtonnement, decomposition), the adjustment process is assumed to run to completion, so that all the allocation and resource decisions can be made on the basis of enough information to guarantee optimal decisions². If, however, decisions must be made before the adjustment process is completed, say, after only a few iterations, then the decisions must be taken with limited information, and thus under conditions of uncertainty. This paper discusses a simple model in an attempt to examine explicitly these problems of uncertainty and limited information. A set of enterprise managers are assumed to produce various commodities, using scarce resources allocated to the enterprises by a resource manager. The enterprise managers also make decisions that affect their individual outputs. Varous kinds of communication among the managers, together with the corresponding information structures, are formulated, including the communication of price and demand messages. Optimal decision rules for the managers are calculated for the objective of maximizing the expected value of an index of total output. (It is assumed that the production functions and the supplies of scarce resources are stochastic, but are observed by the respective managers.) It is shown that optimal decision rules based on a single exchange of price and demand messages, between the resource manager on the one hand and the enterprise managers on the other, produces as good results as rules based on (1) complete information for the resource manager, and (2) information about the supplies of resources on the part of the enterprise managers. Furthermore, these price and demand messages produce approximately fully optimal results when the number of enterprises is large. However, the optimal decisions of the enterprise managers do not maximize profits, at least relative to any price that is the same for all enterprises. An assumption that the production functions are quadratic plays a key role.