Oliver Hart Prize Lecture: Incomplete Contracts and Control

388 

The Nobel Prizes

them onto the same page and avoids bad feeling later on. This is different from 

(but complementary to) the traditional view that contracts are useful to encour-

age noncontractible investments. (In the above example there are no noncon-

tractible investments.)

Once we depart from the case of certainty, it will typically not be possible to 

achieve the first-best. To illustrate this, consider a simplified version of the Hart-

Moore model in which the further assumption is made that S has zero wealth; 

this version will also be helpful for describing some experimental work. Suppose 

that v = 20 for sure but c = 16 with probability π and 10 with probability 1 – π. 

The uncertainty about c will be resolved shortly before date 1 and the realization 

of c is then observable to both parties. However, c is not verifiable. The prob-

ability distribution of c is common knowledge ex ante. Assume further that ex 

post trade is voluntary: either party can refuse to trade and not be penalized, 

perhaps because a third party cannot verify who is responsible for the absence of 

trade. B and S are both risk neutral. There are many more buyers than sellers in 

the date 0 market and so the reservation utility level for S is zero. Finally, ignore 

renegotiation for the moment.

What is an optimal contract for B to offer in this setting? There are only two 

possibilities. Either B wants to ensure trade in both states or only in the low cost 

state. In the first case the optimal contract will specify a price range [10,16] and 

allow B to pick from this range at date 1. That way B can guarantee trade whether 

c is high or low, given that trade is voluntary. Moreover, this is the smallest price 

range that will do the job, which minimizes aggrievement and shading.

With such a contract B will choose p = 10 when c = 10 and p = 16 when c = 

16. In the low cost state S will be aggrieved since B could have been more gener-

ous and have chosen the best outcome for S, p = 16. S’s level of aggrievement is 

6. S punishes B by shading by 6θ, and so B’s net payoff = 10 – 6θ. In the high 

cost state, S is not aggrieved since she receives the highest price permitted by the 

contract. B’s payoff = 4.

The expected payoffs for the two parties are, respectively,

 

U

B

 = (10 – 6θ) (1 – π) + 4π, 

(1)

 

U

S

 = 0. 

(2)

Call this flexible contract, contract 1.

On the other hand, B can choose a contract that permits trade only in the 

low cost state. The best such contract fixes the price at 10. The expected payoffs 

of the two parties are, respectively,

 

U

B

 = 10 (1 – π), 

(3)

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Incomplete Contracts and Control 

389

U

S

 = 0.

(4)

Call this rigid contract, contract 2.

Obviously, contract 2 is better than contract 1 if and only if

 

10(1 – π) > (10 – 6θ)(1 – π) + 4π. 

(5)

This will be true if π is small.

In other words, B will offer S a fixed price contract that precludes trade in the 

high cost state if that state is unlikely to occur. The intuition is simple. It is not 

worth expanding the price range from 10 to [10, 16] just to realize trade in the 

high cost state if it has low probability, given that this causes a large deadweight 

loss from shading in the low cost state that has high probability.

Note also the importance of S’s wealth constraint. In the absence of such a 

constraint, B could offer a contract that specifies p = 16, leading to trade in both 

states. B could charge S upfront 6(1– π) for this contract, thus recouping all of 

S’s expected profit.

This model achieves the main goals described above. First, it is immune 

to the Maskin-Tirole critique. Mechanisms or take-it-or-leave-it offers do not 

achieve the first-best. Indeed, contract 1 contains such a mechanism and leads to 

shading. Second, there can be ex post inefficiency. If (5) holds, B will deliberately 

choose a contract that causes trade not to occur with some probability.

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The Hart-Moore model relies on a number of non-standard assumptions. 

While several of these are similar to behavioral assumptions that have been vali-

dated, there are some significant differences. It therefore seemed desirable to test 

the model directly, and Ernst Fehr, Christian Zehnder, and I have done this in 

the lab.

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 The following is a rough description of the lab experiment in Fehr et al. 

(2011); see also Fehr et al. (2009). (Some simplifications and liberties have been 

taken in describing it.) We divide the student participants into buyers and sellers; 

their roles stay the same during the experiment. Each buyer meets with two sell-

ers, who can bid for the buyer’s contract. (The purpose of this is to achieve ex ante 

competition.) The buyer can choose between two types of contract: one, a flexible 

contract of the form [p,16], the other, a fixed price contract p. Once the contract 

type has been selected the sellers compete for the contract though a clock auc-

tion. The auction determines the level of p: p starts off at 10 and rises a small 

amount every second until one of the sellers accepts. As in many experiments of 

this type the resulting p is close to 10, and we shall treat it as 10 in what follows.

Thus at the end of the auction a seller has agreed to a contract that is either 

[10, 16] if B chose a flexible contract at the earlier stage, or p = 10 if B chose a 

rigid contract. The buyer and the winning seller then move to the next stage, date 

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