The value of information and optimal organization.

The article addresses the issue of optimal organization of production. I compare three organizational forms: centralization (one agent produces different inputs), decentralization (each of two agents produces a different input and contracts directly with the principal), and delegation (two agents produce different inputs, the principal contracts with one of them only). The optimal organizational form depends on the degree of complementarity/substitutability between the inputs in the final use. The degree of complementarity/substitutability also determines whether delegation is payoff equivalent to the two-agent mechanism from the point of view of the principal. In the context of delegation, I consider which of the two agents should serve as the primary contractor. I also address the issue of collusion between the agents in a decentralized organization and characterize the conditions under which a stake of collusion exists.

1. Introduction

One of the central issues in the theory of organizations is how information should be distributed, exchanged, and processed within an organization. Answering this question is important for the design of optimal organizational structures. The relevant literature has explored two different approaches in addressing this issue. The first approach focuses on the cost of information processing, whereas the second approach involves studying incentive problems generated by the asymmetry of information between different parties in an organization.

This article contributes to the second strand of literature. It studies an environment where the principal has to implement a project that requires allocating several tasks to subordinates (or, alternatively, procuring several inputs from providers) who have private information regarding the costs of performing these tasks (producing the inputs). The principal has to determine which organizational structure is optimal and design the contracts with subordinates/providers in an optimal way. I adopt the premise that organizational decisions are more durable than production circumstances, so the choice of an organizational structure has to be made before production costs are realized. A number of questions naturally arise in this context. Should several tasks (production of different inputs) be centralized in the hands of a single agent (supplier), or should those tasks (production of inputs) be allocated across a number of them? Should the agents be organized in a hierarchy or not, and should the amount of communication between them be restricted? For example, a city council can hire a single contractor for a municipal project, split the work between several firms, or allow the primary contractor to subcontract some work to others. A firm may train its employees as specialists in certain types of tasks, so that several employees typically work on a project. Alternatively, employees may be trained as generalists who can perform tasks of different types and handle all the work on some projects. Similar issues arise in a variety of other contexts, including procurement, outsourcing, and regulation.

To address these issues, I examine three organizational forms in the context of a production process requiring two inputs. In a centralized single-agent organization, one agent supplies both inputs. In a decentralized two-agent organization, each of the two agents supplies a different input. Finally, under delegation, two agents supply different inputs, but the principal contracts with one of them and delegates to her the task of contracting with the second agent. The crucial difference between these organizational forms lies in their informational structure. In the single-agent organization, the agent has private information about production costs of both inputs, in the two-agent organization each agent knows only the cost of one input, whereas under delegation the primary contractor serves as an informational intermediary passing the subcontractor's cost information to the principal. Consequently, the relative profitability of these mechanisms depends on the interaction between these two pieces of information.

Intuitively, the value of information to the agent(s) might be either subadditive or superadditive. In the subadditive case, the value of two pieces of information together, as in the single-agent and delegated mechanisms, is lower than the sum of the values of each piece of information used independently, as in the two-agent mechanism. In the superadditive case, the ordering goes in the opposite way. Put simply, the main issue is whether from an agent's point of view the knowledge of another piece of information increases the value of the first piece of information or decreases it. (2) Because the principal's interests are the opposite of the agent(s)'s interests, the principal prefers informational centralization if the value of information is subadditive for the agents. Conversely, the principal prefers informational decentralization if the value of information is superadditive.

The main insight of this article is that the degree of complementarity or substitutability between the inputs (3) determines whether the value of information is sub- or superadditive. Precisely, under complementarity or small degree of substitutability the value of information is subadditive, provided that the two inputs are not too asymmetric in the final use, and it is superadditive when the degree of substitutability is sufficiently large.

To understand why this is so, consider the value of information in a single-agent mechanism. When the cost of an input is low, the agent earns a rent on this information. The value of this rent is equal to the surplus obtained by misrepresenting this cost as high, and is therefore proportional to the quantity of this input delivered under high cost.

Now consider the effect of misrepresenting a low cost of one input on the value of information about the second input. First, incentive compatibility of the mechanism requires the quantity of an input to decrease in the agent's marginal cost of production. Second, in an efficient ordering, under complementarity (substitutability), the optimal quantity of the second input is increasing (decreasing) in the quantity of the first input. So, under complementarity, misrepresenting the cost of one input upward causes the quantity of the second input to go down, and therefore reduces the informational rent on the second piece of information. Under substitutability, such misrepresentation has the opposite effect because the optimal quantity of an input is increasing in the cost of the second input.

Thus, the reported cost of one input affects the value of information about the cost of the other input. We will refer to this as an "internalization factor," because a single agent internalizes this effect on her total payoff. In contrast, in the two-agent mechanism, each agent exploits the value of her information independently taking the other agent's strategy as given, and this effect is not internalized. Therefore, under complementarity (substitutability), the internalization factor tends to make the value of information subadditive (superadditive).

The other factor affecting the relative performance of the single-agent and two-agent mechanisms is the difference in the structure of incentive constraints. In contrast to the two-agent mechanism, a single agent can manipulate both pieces of information, that is, she can misrepresent production costs of both goods at the same time. So, a larger set of incentive constraints has to be satisfied in the single-agent mechanism. We refer to this as an "extra deviation" factor. This factor makes each piece of information more valuable when the second piece is also known. Hence, it tends to make information superadditive.

To summarize, whether the value of information is sub- or superadditive, and hence which organizational structure is optimal, depends on the relative strength of the internalization and the extra deviation factors. The single-agent mechanism typically dominates the two-agent one under complementarity, because the internalization factor favoring the single-agent mechanism is especially potent in this case. The principal is also able to leverage the effect of the internalization factor and design a mechanism in which the value of information is subadditive under separability and even under a small degree of substitutability. In the latter case, the mechanism involves additional efficiency losses, as the quantity of one input is set to increase in the quantity of the other input--the opposite of the efficient ordering. But because the degree of substitutability is low, these efficiency losses are small, and the single-agent mechanism still dominates the two-agent one.

Nevertheless, the extra deviation factor can overturn the ranking of organizational forms under complementarity when there is a strong asymmetry between inputs and the change in quantity of one input affects the marginal product of this input to a lesser degree than the marginal product of the other input. In this case, it becomes very attractive for a single agent to make a joint misrepresentation of the combination of low and high costs as high and low, respectively. Proposition 2 provides the condition under which this extra deviation factor makes the two-agent mechanism more profitable for the principal.