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Article Excerpt
We analyze a cheap talk game with partial commitment by the principal. We first treat the principal's commitment power as exogenous and then endogenize it in an infinitely repeated game. We characterize optimal decision making for any commitment power and show when it takes the form of threshold delegation--in which case the agent can make any decision below a threshold--and centralization--in which case the agent has no discretion. For small biases, threshold delegation is optimal for any smooth distribution. Outsourcing can only be optimal if the principal's commitment power is sufficiently small.
1. Introduction
The internal allocation of decision rights is a key determinant of the behavior of firms. Although owners have the formal authority to make all decisions on behalf of their firms, they typically delegate at least some important decision rights to their employees. These employees, however, often have consistent biases and can be expected to make different decisions than the owners would (Jensen, 1986). An understanding of what determines the internal allocation of decision rights is therefore a prerequisite for understanding, and potentially being able to predict, the decisions that firms make, such as how much to invest and how many workers to hire and fire. In this article, we investigate the optimal allocation of decision rights within firms. In particular, we investigate how the owner of a firm should delegate decision rights to a biased employee.
Although the formal authority to make decisions is concentrated at the top of firms, the information needed to make effective use of this authority is often dispersed throughout their ranks. The legal right to decide on the allocation of capital, for instance, resides with the owners of firms but CEOs, division managers, and other employees are often better informed about the profitability of different investment projects. The benefit of delegating decision rights is that it allows the owners to utilize the specific knowledge that their employees might have (Holmstrom, 1977, 1984; Jensen and Meckling, 1992).
There are two main difficulties in delegating decision rights, however. First, as mentioned above, there is ample evidence which suggests that employees have consistent biases and are therefore likely to make different decisions than the owners would want them to. Agency costs therefore place a limit on the ability of owners to delegate decision rights (Holmstrom, 1977, 1984; Jensen and Meckling, 1992). Second, delegated decision rights are always "loaned, not owned" (Baker, Gibbons, and Murphy, 1999). In other words, whereas owners can delegate decision rights ex ante, they can always overrule the decisions that employees make ex post. Anticipating the possibility of being overruled, the employees in turn may act strategically and, as a result, their specific knowledge might not get used efficiently. Imperfect commitment therefore places a second limit on the ability of owners to delegate decision rights (Baker, Gibbons, and Murphy, 1999).
Because of the presence of agency costs and the lack of perfect commitment, owners rarely engage in complete delegation, that is they rarely delegate decision rights without putting in place rules and regulations that constrain the decisions their employees can make. Consider, for instance, the decision over the allocation of capital which is often delegated to lower-level managers and, in particular, to division managers. Although in some firms these division managers have almost full discretion in deciding between different investment projects, in most they face a variety of constraints. In some firms, for instance, division managers are allowed to decide on investment projects that affect the daily operation of their divisions but not on those that are deemed to affect the future of the firm as a whole. In other firms, division managers can decide on investment projects that do not exceed a certain threshold size, and their superiors decide on larger projects. (1) In this article, we show that many of the organizational arrangements that we observe in practice arise optimally in a model in which a principal with imperfect commitment delegates decision rights to a better-informed but biased agent.
Our analysis is based on a model with three main features. (i) A firm that consists of a principal and an agent has to implement a project and the principal has the formal authority to decide which project is implemented. The potential projects differ on one dimension, for instance investment size, and the principal and the agents have different preferences over this dimension. (ii) The agent is better informed about the projects' payoffs than the principal. In particular, only the agent observes the state of the world which determines the identity of his preferred project and that of the principal. Before making her decision the principal asks the agent for a recommendation. The principal then either rubber-stamps the recommendation or overrules it and implements another project. (iii) The principal has some commitment power. In particular, before the agent makes his recommendation, the principal makes a promise about how she will respond to the agent's recommendation. In case the principal reneges on this promise, for instance by not rubber-stamping a recommendation that she promised to approve, she incurs a certain cost. This cost measures the principal's commitment power: the higher the cost, the more commitment power the principal has. We interpret this cost as the damage that an agent can impose on the principal through unproductive behavior in a repeated relationship. We first follow MacLeod (2003) in considering a static model in which the cost of conflict is exogenous and then develop a repeated game in which this cost is endogenously determined.
Although the principal always has the formal authority to decide on projects, she can engage in many different types of relational delegation. In other words, she can implicitly commit to many different decision rules that map the agent's recommendations into decisions. For instance, she can engage in complete delegation by committing herself to always rubber-stamp the agent's recommendation. Other possibilities include threshold delegation--in which case the principal rubber-stamps the agent's recommendation up to a certain size and implements her preferred project if he recommends a project that is above the threshold--and menu delegation--in which case the principal rubber-stamps the agent's recommendation only if he proposes one of a finite number of projects. Of course, the principal can also choose to ignore the agent's recommendation altogether and simply implement the project that maximizes her expected payoff given her prior. In other words, she can engage in centralization.
Should the principal centralize or delegate? And if she delegates, should she engage in complete delegation, threshold delegation, or some other form of delegation? The key tradeoff that the principal faces when she considers the many different organizational arrangements is between the direct cost of biasing her decisions in favor of the agent and the indirect benefit of inducing the agent to reveal more information. Moreover, when optimizing this tradeoff, the principal must keep in mind that the extent to which she is able to bias her decisions is limited by her potentially imperfect commitment power. We show that in many cases the organizational arrangements that the principal chooses in our setting are commonly observed in the real world. In particular, we show that centralization, threshold delegation, and menu delegation are often optimal and that which one of these arrangements is optimal depends only on the principal's commitment power, on the one hand, and a simple condition on the agents' bias and the distribution of the state space, on the other. Moreover, we show that for small biases, threshold delegation is optimal for any smooth distribution. These results are consistent with the pervasive use of threshold delegation in organizations. Having derived our main characterization result we then investigate further implications, including the effects of changes in the bias and the amount of private information on the optimal organizational arrangement. Finally, we show that irrespective of the commitment power of the principal, complete delegation is never optimal and that outsourcing can only be optimal if the principal's commitment power is sufficiently small.
In the next section we discuss the related literature. In Section 3, we then present our basic model in which the principal's commitment power is exogenously given. We analyze this model in Sections 4 and 5 and characterize the optimal organizational arrangements for any given level of commitment. In Section 6, we then embed our basic model in a repeated game in which the principal's commitment power is endogenously determined. There we show that the optimal relational contract corresponds to optimal organizational arrangements in the static model for an appropriately specified discount rate. The repeated game allows us to derive additional implications, which we discuss in Section 7. Finally, we conclude in Section 8. The proofs of Propositions 3 and 4 are sketched in the Appendix. Full proofs of all propositions are posted on our websites as www.kellogg.northwestern.edu.
2. Related literature
Suppose an organization, consisting of a principal and an agent, has to make a decision. The principal and the agent have different preferences over the decision and only the agent observes the state of the world which determines the principal's and the agent's preferred projects. A large number of papers have analyzed this basic problem and they can be categorized in two dimensions: (i) whether or not they allow for transfers between the principal and the agent and (ii) the extent of the principal's commitment power.
Our article contributes to the strand of the literature which argues that in many environments, transfers between the principal and the agent are difficult or impossible. Within this strand of the literature, one can distinguish between delegation and cheap talk models. In the cheap talk models that follow Crawford and Sobel (1982), principals cannot commit to arbitrary decision rules, that is they cannot commit to act on the information they receive in a prespecified way. In contrast, in the delegation models that follow Holmstrom (1977, 1984), the principal can commit to a decision rule. Holmstrom (1977, 1984) considers a general version of the setup described above and proves the existence of an optimal delegation set or, equivalently, an optimal decision rule. He then characterizes optimal interval delegation sets, that is, delegation sets in which the agent can choose any decision from a specific interval. (2) Armstrong (1995) considers a model similar to Holmstrom's (1977, 1984) and allows for uncertainty over the agent's preferences. Like Holmstrom (1977, 1984), he focuses on interval delegation. In a setting in which the players' preferred decisions are linear functions of the state and the state is uniformly distributed, Melumad and Shibano (1991) characterize the optimum among all delegation sets. In a recent paper, Alonso and Matouschek (2005) solve for the optimal delegation set in a setting that allows for more distributions and for arbitrary continuous state-dependent biases. In a similar setting, but allowing for more general distributions, Martimort and Semenov (2006) provide a sufficient condition for threshold delegation to be optimal. Because we allow for different degrees of commitment by the principal, varying from no commitment all the way to perfect commitment, our article bridges the cheap talk and delegation literatures. Instead of making assumptions about what the principal can and cannot commit to, we endogenize her commitment power and characterize the optimal decision rule for any amount of commitment power.
The second strand of the literature that analyzes the principal-agent problem described above does allow for transfers. Ottaviani (2000) and Krishna and Morgan (2006), in particular, both allow for message-contingent transfers but make different assumptions about the principal's commitment power. In particular, Krishna and Morgan (2006) focus on the case in...
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