RAND Journal of Economics Vol. 18, No. 2, Summer 1987 Competition for agency contracts R. Preston McAfee* and John McMillan** This article introduces a market for the services of agents into a principal-agent model. The principal and the potential agents are risk neutral. The contract trades off adverse selection against moral hazard. In a broad range of circumstances the optimal contract is linear in the outcome. In an incentive-compatible contract the more able is an agent, the larger is his contractual share of his marginal output, thus, a more able agent is induced to work at a rate closer to the first-best. 1. Introduction c When a principal contracts with an agent for the provision of some good or service, the contract often does not specify a fixed price. Instead, the contract contains provisions for price adjustment. For example, when a firm subcontracts some of its input requirements to another firm, or when a government contracts for the production of a public good, the contract often provides for the price to be adjusted in response to unpredictable changes in the supplier's costs. A salesman's remuneration is usually dependent, via commissions, on the amount he sells; but often he also receives a fixed sum regardless of the level of his sales. The contracts between publisher and author, franchisor and franchisee, landlord and share- cropper, and patent holder and licensee similarly often have both fixed and variable com- ponents.' As Arrow (1985, p. 44) notes, "a fee function is a significant departure from the arms-length fixed-price relation among economic agents usually postulated in economic theory." Typically, the fee functions used in practice are simple: contracts involving royalties or commissions make the payment linear in the output. At first glance, it might seem that contractual provisions that lessen the agent's re- sponsibility for his own actions, such as provisions for price adjustment in response to cost fluctuations, or fixed payments to salesmen, cannot be in the principal's interest. To some extent the costs incurred or the sales achieved depend upon the effort made by the agent: * University of Western Ontario. ** University of California, San Diego and University of Western Ontario. We thank Bengt Holmstrom, Glenn MacDonald, Paul Milgrom, David Sappington, David Sibley, Alan Slivinski, Jean Tirole, and the Editorial Board for useful comments. In articles developed simultaneously, Laffont and Tirole (1985) and Riordan and Sappington (1987) derived results similar to ours. ' A share contract of some historical consequence was the agreement between the Spanish Crown and Chris- topher Columbus, under which Columbus was entitled to 10% of the output of the territories he discovered (Elliot, 1970, p. 61). 296 McAFEE AND McMILLAN / 297 in other words, there is moral hazard. Such contractual provisions weaken the agent's in- centives to act as the principal would want. The principal-agent literature (Harris and Raviv, 1979; Holmstrdm, 1979; Shavell, 1979; MacDonald, 1984; Holmstrom and Milgrom, 1987) provides one possible explanation for price-adjustment provisions. If the agent is more risk averse than is the principal, then it is in their mutual interest to share the burden of the risk. The principal, in designing the contract that is best for him, trades off risk sharing against moral hazard. Often, however, the parties to a contract are large, and the risks associated with any one contract are small relative to their overall operations. In such cases contractual provisions for price adjustment cannot be explained as risk-sharing devices. This article offers an al- ternative principal-agent model, applicable when both principal and agent are risk neutral. The model provides an explanation of contractual provisions for price adjustment without appealing to risk aversion. We introduce a market for the services of agents. Potential agents compete with each other for the contract with the principal. The potential agents have different types (for example, innate ability) that the principal cannot observe: in other words, there is adverse selection in the market for agents' services. The principal designs a contract that exploits the competition among the potential agents and induces them to reveal their types. Instead of trading off risk sharing against moral hazard, as in the usual principal-agent model, in this setting the contract trades off adverse selection against moral hazard.2 Arrow (1985, p. 48) in evaluating principal-agent theory notes that the principal-agent relationships observed in the real world differ from those predicted by principal-agent theory: Most importantly, the theory tends to lead to very complex fee functions. It turns out to be difficult to establish even what would appear to be common-sense properties of monotonicity and the like. We do not find such complex relations in reality. Holmstrbm and Milgrom (1987) make a similar point. In contrast, we shall show that the contract that, for the principal, optimally trades off adverse selection against moral hazard can be relatively simple. In a broad set of circumstances, the predicted contract is linear in the observed outcome. The contract varies with the selected agent's type: in an incentive-compatible contract, the more efficient is an agent, the larger is his contractual share of his marginal output. Thus, the contract screens the agents according to their abilities, and a more efficient agent is induced to work at a rate closer to the first-best. But except when the selected agent has the highest possible efficiency, the contract elicits less than the ideal amount of effort. Despite the principal's ability to commit himself to his mechanism, the asymmetry of information leaves the selected agent with some of the gains from trade. 2. Adverse selection and moral hazard * A risk-neutral principal wishes to contract with a single agent. There are n risk-neutral potential agents who compete for the contract. The potential agents have different charac- teristics, denoted z (measuring, for example, efficiency, ability, or expected production cost). Each potential agent knows only his own type z; the other potential agents and the principal perceive types as being independently drawn from a distribution G(z), with density g(z). Thus, differences among the potential agents are assumed to reflect inherent differences in their productivity, so that, after learning that he has an unusually high or low z, a potential 2 The tradeoff between adverse selection and moral hazard was also modelled in our earlier article (McAfee and McMillan, 1986). That model was more general than the present one in allowing the potential agents to be risk averse. But it considered only a restricted class of contracts, whereas the present analysis solves for the contract that is fully optimal given the informational constraints. 298 / THE RAND JOURNAL OF ECONOMICS agent has no reason to revise his estimates of the others' z values.3 Let the support of g be an interval [z0, z1]. The principal, having announced the contractual payment terms, asks the potential agents to report their types. Denote by z^ an agent's reported type. On the basis of these reports, the principal selects one agent. The agent who wins the contract chooses a level of effort (possibly multidimensional), which is not directly observable by the principal. Output x, which is observed by the principal, depends on the agent's effort and ability, as well as on a random variable. We leave implicit in the notation both the effort and the random shock, and depict the agent as choosing an expected level of output pt. We assume C(Q, z) is the cost, in monetary terms, to an agent of obtaining a given expected output ,t when his type is z. We assume that higher types have a lower cost and a lower marginal cost: Cj(M, z) < 0, C,,(,t, z) < 0, where subscripts denote partial derivatives. We assume also that the marginal cost of output is positive and increasing: C,(M, z) > 0, C"(tt, z) > 0.4 The assumptions of risk neutrality and independent types imply that the principal would gain nothing by making the payment to the selected agent depend on the other potential agents' reports, or by requiring payments from the other potential agents. This is so since under these two assumptions any payment scheme that depends on the reports of the other potential agents can be replaced by one with the same expected payment, given the selected agent's type, without affecting the incentives.5 Thus, we assume that the principal makes his payment to the selected agent depend only upon the agent's reported type and the observed outcome. Let S(z^, x) denote the payment function to which the principal commits himself. Thus, the principal's return is x - S(z^, x), and the selected agent's return is S(z, x) - C(t, z). The net (social) expected return is ut - C(M, z), which we presume is positive for some z, tt. This problem involves both adverse selection (since the principal cannot observe the potential agents' types) and moral hazard (since the principal cannot observe the selected agent's action). The purpose of this article is to derive the principal's optimal payment function S(z^, x). 3. The agent's optimization * In this section we shall examine the contract offered by the principal in terms of the action tt that an agent of type z chooses, that is, in terms of the function pt(z). We show that 3 This is the independent-private-values assumption: for a thorough discussion of the meaning and the lim- itations of this assumption, see Milgrom and Weber (1982, pp. 1090-1098). 4 We thank Paul Milgrom for the observation that depicting the agent as choosing expected output simplifies the analysis.