Bengt Holmström Prize Lecture: Pay for Performance and Beyond

416 

The Nobel Prizes

employee working for a manager; a lawyer serving a client; a doctor treating a 

patient; or a CEO serving the board of a company, to name a few.

There are two challenges when designing an optimal incentive scheme for 

effort. First, the agent finds it privately costly to provide the service, at least 

beyond some base level, so a financial inducement based on performance is 

needed. But performance is imperfectly measured, so variable pay will induce 

risk on the agent. Since the agent is risk averse, there is a trade-off between risk 

and incentive. How should it be optimally solved?

One could approach this problem by studying simple incentive schemes such 

as a linear incentive in addition to a fixed wage, or a bonus for performance 

beyond some minimum standard.

1

 The problem with using a particular func-

tional form is that the analysis will not tell us why different incentives are used 

in different contexts. Also, fixing the form of the incentive pay may silence trade-

offs that are essential for understanding the underlying incentive problem. This 

makes it valuable to study the problem without functional restrictions.

Let me turn to a simple, generic formulation of the principal-agent relation-

ship. The agent chooses an unobserved level of effort e. The agent’s choice of 

effort leads to a payoff x = x(e,ε), where ε captures random external factors such 

as market conditions or measurement errors that the agent does not control 

directly. I will often work with the additive specification x = e + ε.

As Mirrlees ([1975] 1999) noted, it is technically convenient and more ele-

gant to view the agent as choosing a distribution over x. For a fixed choice e, the 

distribution over ε induces a distribution over x, denoted F(x|e). This eliminates ε

and gives a simpler and, as we will see, much more informative characterization, 

though the explicit dependence on ε can be helpful for thinking about particular 

contexts.

2

Before the agent acts, the principal offers the agent an incentive contract s, 

which pays the agent s(x) when the realized payoff is x. The principal keeps the 

residual x − s(x). The utilities of the agent and the principal are, respectively, 

U = u(s(x)) − c(e) and V = x − s(x), so the principal is risk neutral and the agent 

(in general) risk-averse. The agent’s utility function is additively separable, which 

is restrictive but commonly used.

The principal and the agent are symmetrically informed at the time they sign 

the contract (this is what makes the problem one of moral hazard). In particular, 

they know each other’s utility functions and hold the same beliefs about the dis-

tributions F(x|e). The principal can therefore forecast the agent’s behavior given 

s(x) even though she cannot observe the agent’s choice of effort.

The incentive scheme s(x) must provide the agent an expected utility that is 

at least as high as the agent can get elsewhere. The agent’s participation requires 

---

Pay For Performance and Beyond 

417

the principal to consider the impact s(x) has on the agent’s expected utility. The 

agent’s burden from extra risk and extra effort is ultimately borne by the princi-

pal. Finding the best contract is therefore a shared interest in the model (but not 

necessarily in practice).

To determine the principal’s optimal offer, it is useful to think of the principal 

as proposing an effort level e along with an incentive scheme s(x) such that the 

agent is happy to choose e, that is, s(x) and e are incentive compatible. This leads 

to the following program for finding the optimal pair {s(x),e}:

 

Max E[x − s(x)|e], subject to 

(1)

 

E[u(s(x)) − c(e)|e] ≥ E[u(s(x)) − c(e′)|e′] for e′ ≠ e, and 

(2)

 

E[u(s(x)) − c(e)|e] ≥ U. 

(3)

The first constraint assures that e is optimal for the agent. The second con-

straint guarantees that the agent gets at least his reservation utility U if he chooses 

e and therefore will accept the contract. I will assume that there exists an optimal 

solution to this program.

3

B.  First-best Cases

Before going on to analyze the optimal solution to the second-best program 

(1)–(3) it is useful to discuss some cases where the optimal solution coincides 

with the first-best solution that obtains when the incentive constraint (2) can 

be dropped, because any effort level e can be enforced at no cost. Because the 

principal is risk neutral, the first-best effort, denoted e

FB

, maximizes E(x|e) − c(e).

A first-best solution can be achieved in three cases:

I.  There is no uncertainty.

II.  The agent is risk neutral.

III.  The distribution has moving support.

If (I) holds, the agent will choose e

FB

 if he is paid the fixed wage w = 

u

–1

(U + c(e

FB

)) whenever x ≥ e

FB

 and nothing otherwise. The wage w is just 

sufficient to match the agent’s reservation utility U. If (II) holds, the principal 

can rent the technology to the agent by setting s(x) = x − E(x|e

FB

) + w. As a risk-

neutral residual claimant the agent will choose e

FB

 and will earn his reservation 

utility U as in case (I).

The third case is the most interesting and also hints at the way the model 

reasons. For concreteness, suppose x = e + ε with ε uniformly distributed on [0, 

---