Vertical and Horizontal Communication in Economic Processes

Abstract

Two fundamentally different concepts of communication have appeared in the literature on economic adjustment processes. One is vertical communication (vc) in which all agents send messages to and receive messages from a central agent often called the auctioneer, helmsman or central planner. Typically, there is a considerable amount of common information available, usually in the form of prices which all agents observe. Often there is some central coordination of actions. An agent has little direct contact with agents other than the central agent. Examples are the tatonnement model of market adjustment (Arrow and Hurwicz (1959)) and models of decentralized planning (Arrow and Hurwicz (1960), Heal (1969) and Malinvaud (1967)). The second concept is horizontal communication (hc) in which all message exchange occurs through direct contact between agents. There is no one agent involved in every message exchange as in vertical communication. There is little common information and no central coordination of actions. Examples are models of general equilibrium under search behaviour (Diamond (1971), Fisher (1973) and Mortensen (1973)) and models of sequential trading (Feldman (1973)). In this paper we compare the value of information generated by some frequently used examples of vertical and horizontal communication. We adopt Marshak and Radner's model of a team in which conflict is absent in order to concentrate on the informational aspects of communication. The apparent need for common information and central coordination when organization-wide constraints are present suggests that vertical communication processes should perform better than horizontal communication. Our principle result is that, for truncated adjustment processes, limited horizontal communication may be more effective than limited vertical communication even when there is a team-wide constraint to satisfy. However, for large teams, hc can be no more effective than vc. These conclusions are the result of an analysis of specific examples of a team resource allocation model introduced by Groves and Radner (1972) and Radner (1972). Our examples also demonstrate that in order to satisfy resource constraints in a teamdecision model, it is not necessary either to have one agent control all decisions entering the constraint (as in quantity planning) or restrict a member's actions entering the constraint to depend only on events which all members can observe (as in planning by pricing). Many procedures, such as tatonnement, decentralized planning and bilateral exchange have been designed to compute optimal solutions to the problem of allocation resources within an organization. These procedures consist of an iterative exchange of messages between agents such that the messages converge to some value. This equilibrium message is then translated by an outcome function into actions which are optimal. Because of the costs involved in communication, such procedures will, in practice, be truncated before the equilibrium message is known. If a process is truncated, the outcome rule applied to the current messages may not provide feasible actions.- In tatonnement, for example, positive