\documentstyle[12pt,epsf]{msart} \begin{document} \textheight 9in \setcounter{section}{8} \setcounter{page}{249} \noindent march 1998 \section*{ 8 TOPICS IN MORAL HAZARD } \noindent {\bf Unravelling the Truth when Silence is the Only Alternative} Suppose that Nature uses the uniform distribution to assign the variable $\theta$ some value in the interval $[0, 10]$ and the agent's payoff is increasing in the principal's estimate of $\theta$. Usually we assume that the agent can lie freely, sending a message $m$ taking any value in $[0,10]$, but let us assume instead that he cannot lie, although he is free to conceal information. Thus, if $\theta = 2$, he can send the uninformative message $m \geq 0$ (equivalent to no message), or $m \geq 1$, or $m=2$, but not the lie $m \geq 4$. When $\theta=2$ the agent might as well send a message that is the exact truth: ``$m=2$''. If he were to choose ``$m \geq 1$'', for example, the principal's first thought might be to estimate $\theta$ as the average value of the interval $[1,10]$, which is 5.5. But the principal would realize that no agent with a value of $\theta$ greater than 5.5 would want to send that message in a Nash equilibrium. This realization restricts the possible interval to [1, 5.5], which in turn has an average of 3.25. But then no agent with $\theta > 3.25$ would send the message ``$m \geq 1$''. The principal can continue this process of logical {\bf unravelling} to conclude that $\theta = 1$. The message ``$m \geq 0$'' would be even worse, making the principal believe that $\theta = 0$. In this model, ``No News is Bad News.'' The agent would therefore not send the message ``$m \geq 1$'' and he would be indifferent between ``$m=2$'' and ``$m \geq 2$'' because the principal would make the same deduction from either message. \newpage \bigskip \noindent {\bf The Revelation Principle} \noindent The principal might choose to offer a contract that induces the agent to lie in equilibrium, since he can take lying into account when he designs the contract, but this complicates the analysis. Each state of the world has a single truth, but a continuum of lies: generically speaking, almost everything is false. The revelation principle helps us simplify. \noindent {\bf The Revelation Principle.} {\it For every contract $w(q,m)$ that leads to lying (that is, to $m \neq \theta$), there is a contract $w^*(q,m)$ with the same outcome for every $\theta$ but no incentive for the agent to lie.} Applied to concrete examples, the revelation principle may seem obvious. Suppose we are concerned with the effect on the moral climate of cheating on income taxes, but anyone who makes \$70,000 a year can claim he makes \$50,000 and the government does not have the resources to catch him. The Revelation Principle says that we can rewrite the tax code to set the tax to be equal for taxpayers earning \$70,000 and for those earning \$50,000, and the same amount of taxes will be collected without anyone having incentive to lie. Applied to moral education, the principle says that the mother who agrees never to punish her daughter if she tells her all her escapades will never hear any untruths. Clearly, the principle's usefulness is not so much to improve outcomes as to simplify contracts. The principal (and the modeller) need only look at contracts which induce truthtelling, so the relevant strategy space is shrunk and we can add a third constraint to the incentive compatibility and participation constraints to help calculate the equilibrium: \newpage \subsection{ An Example of Moral Hazard with Hidden Knowledge: ``The Salesman Game''} %8.2 \begin{center} {\bf ``The Salesman Game''} \end{center} {\bf Players}\\ A manager and a salesman. \noindent {\bf Order of Play}\\ (1) The manager offers the salesman a contract of the form $w(q,m)$, where $q$ is sales and $m$ is a message.\\ (2) The salesman decides whether or not to accept the contract.\\ (3) Nature chooses whether the customer is a $Bonanza$ or a $Pushover$ with probabilities 0.2 and 0.8. Denote the state variable ``customer status'' by $\theta$. The salesman observes the state, but the manager does not.\\ (4) If the salesman has accepted the contract, he chooses his sales level $q$, which implicitly measures his effort. \noindent {\bf Payoffs}\\ The manager is risk neutral and the salesman is risk averse. If the salesman rejects the contract, his payoff is $\bar{U}= 8$ and the manager's is zero. If he accepts the contract, then\\ \begin{tabular}{ll} $ \pi_{manager}$ & $= q - w$.\\ $\pi_{salesman}$ &$ = U(q, w, \theta)$, where $\frac{\partial U}{\partial q} < 0, \frac{\partial^2 U}{\partial q^2} < 0, \frac{\partial U}{\partial w} > 0, \frac{\partial^2 U}{\partial w^2} < 0.$ \end{tabular} \bigskip \newpage \begin{equation} \label{e3} {\rm Separating\;\; Contract } \left\{ \begin{array}{ll} {\rm Agent\;\; announces}\;\; {\it Pushover}:& \begin{array}{ll} w =& \left\{ \begin{array}{l} 0 \; {\rm if}\; q < q_1.\\ w_1 \; {\rm if }\; q \geq q_1.\\ \end{array} \right. \\ \end{array} \\ {\rm Agent\;\; announces\;\;} { \it Bonanza}: & \begin{array}{ll} w = & \left\{ \begin{array}{l} 0 \; {\rm if}\; q < q_2.\\ w_2\; {\rm if} \; q \geq q_2. \end{array} \right. \end{array} \end{array} \right. \end{equation} \newpage \begin{center} {\bf ``The Repossession Game''} \end{center} {\bf Players}\\ A bank and a consumer. \noindent {\bf Order of Play}\\ (1) The bank can do nothing or can offer the consumer an auto loan which allows him to buy a car that costs 11, but requires him to pay back $L$ or lose possession of the car to the bank. \\ (2) The consumer accepts or rejects the loan.\\ (3) The consumer chooses to $Work$, for an income of 15, or $Play$, for an income of 8. The disutility of work is 5. \\ (4) The consumer repays the loan or defaults. \\ (4a) In one version of the game, the bank offers to settle for amount $S$ and leave possession of the car to the consumer.\\ (4b) The consumer accepts or rejects the settlement $S$. \\ (5) If the bank has not been paid $L$ or $S$, it repossesses the car. \noindent {\bf Payoffs}\\ If the bank does not make any loan or the consumer rejects it, both players' payoffs are zero. The value of the car is 12 to the consumer and 7 to the bank, so the bank's payoff if a loan is made is $ \pi_{bank}=$ $\left| \begin{tabular}{ll} $L-11$ & if the original loan is repaid\\ $S-11$ & if a settlement is made\\ $7-11$ & if the car is repossessed. \end{tabular} \right.$ If the consumer chooses $Work$ his income $W$ is 15 and his disutility of effort $D$ is $-5$. If he chooses $Play$, then $W=8$ and $D=0$. His payoff is $\pi_{consumer}=$ $\left| \begin{tabular}{ll} $W+12-L-D$ & if the original loan is repaid\\ $W+12-S-D$ & if a settlement is made\\ $W-D$ & if the car is repossessed. \end{tabular} \right.$ \newpage \noindent {\bf ``Repossession Game I''} The first version of the game does not allow renegotiation, so moves (4a) and (4b) are dropped from the game. In equilibrium, the bank will make the loan at a rate of $L=12$, and the consumer will choose $Work$ and repay the loan. Working back from the end of the game in accordance with sequential rationality, the consumer is willing to repay because by repaying 12 he receives a car worth 12.\footnote{As usual, we could change the model slightly to make the consumer strongly desire to repay the loan, by substituting a bargaining subgame that splits the gains from trade between bank and consumer rather than specifying that the bank make a take-it-or-leave-it offer. See Section 4.3. } He will choose $Work$ because he can then repay the loan and his payoff will be 10 $(= 15 + 12-12 -5 )$, but if he chooses $Play$ he will not be able to repay the loan and the bank will repossess the car, reducing his payoff to 8 $(= 8 -0 )$. The bank will offer at loan at $L=12$ because the consumer will repay it and that is the maximum repayment to which the consumer will agree. The bank's equilibrium payoff is 1 $(=12-11)$. This is an efficient outcome because the consumer does buy the car, which he values at more than its cost to the car dealer, although it is the bank rather than the consumer that gains the surplus, because of the bank's bargaining power over the terms of the loan. \newpage \noindent {\bf ``Repossession Game II''} The second version of the game does allow renegotiation, so moves (4a) and (4b) are added back into the game. Renegotiation turns out to be harmful, because it results in an equilibrium in which the bank refuses to make a loan, reducing the payoffs of bank and consumer to (0,10) instead of (1,10); the gains from trade are lost. The equilibrium in ``Repossession Game I'' breaks down because the consumer would deviate by choosing $Play$. In ``Repossession Game I'', this would result in the bank repossessing the car, and in ``Repossession Game II'', the bank still has the right to do this, for a payoff of $-4\; (=7-11)$. If the bank chooses to renegotiate and offer $S=8$, however, this settlement will be accepted by the consumer, since in exchange he gets to keep a car worth 12, and the payoffs of bank and consumer are $-3\; (=8-11)$ and 12 $(= 8 + 12-8 )$. Thus, the bank will renegotiate, and the consumer will have increased his payoff from 10 to 12 by choosing $Play$. Looking ahead to this from move (1), however, the bank will see that it can do better by refusing to make the loan, resulting in the payoffs (0,10). The bank cannot even break even by raising the loan rate $L$. If $L=30$, for instance, the consumer will still happily accept, knowing that when he chooses $Play$ and defaults the ultimate amount he will pay will be just $S=8$. Renegotiation has a paradoxical effect. In the subgame starting with consumer default it increases efficiency, by allowing the players to make a pareto improvement over an inefficient punishment. In the game as a whole, however, it reduces efficiency by preventing players from using punishments to deter inefficient actions. This is true of any situation in which punishment imposes a deadweight loss instead of being simply a transfer from the punished to the punisher. This may be why American judges are less willing than the general public to impose punishments on criminals. By the time a criminal reaches the courtroom extra years in jail have no beneficial effect (incapacitation aside) and impose real costs on both criminal and society, and judges are unwilling to impose sentences which in each particular case are inefficient. This game also illustrates the difficulty of deciding what ``bargaining power'' means. This is a term that is very important to how many people think about law and public policy but for which people only have hazy definitions in mind. Chapter 11 will analyze bargaining in great detail, using the paradigm of splitting a pie, and the natural way to think of bargaining power is as the ability to get a bigger share of the pie. Here, the pie to be split is the surplus of 1 from the consumer's purchase of a car at cost 11 which will yield him 12 in utility. Both versions of ``The Repossession Game'' give all the bargaining power to the bank in the sense that where there is a surplus to be split, the bank gets 100 percent of it. But this does not help the bank in ``Repossession Game II'', because the consumer can put himself in a position where the bank ends up a loser from the transaction despite its bargaining power. \newpage \subsection{Efficiency Wages} \noindent The next three sections are about remedies for moral hazard that can be applied to either hidden actions or hidden knowledge. Most of the illustrations will be of hidden actions, but usually ``low effort'' can be replaced by ``lying about the hidden knowledge.'' Shapiro \& Stiglitz (1984) show how involuntary unemployment can be explained by a principal-agent model. When all workers are employed at the market wage, a worker who is caught shirking and fired can immediately find another job just as good. Firing is ineffective and effective penalties like boiling in oil are excluded from the strategy spaces of legal businesses. Becker \& Stigler (1974) have suggested that workers post performance bonds, but if workers are poor this is impractical. Without bonds or boiling in oil, the worker chooses low effort and receives a low wage. To induce a worker not to shirk, the firm can offer to pay him a premium over the market-clearing wage, which he loses if he is caught shirking and fired. If one firm finds it profitable to raise its wage, however, so do all firms. One might think that after the wages equalized, the incentive not to shirk would disappear. But when a firm raise its wages, its demand for labor falls, and when all firms raise their wages, the market demand for labor falls, creating unemployment. Even if all firms pay the same wages, a worker has an incentive not to shirk, because if he were fired he would stay unemployed, and even if there is a random chance of leaving the unemployment pool, the unemployment rate rises sufficiently high that workers choose not to risk being caught shirking. The equilibrium is not first-best efficient, because even though the marginal revenue of labor equals the wage, it exceeds the marginal disutility of effort, but it is efficient in a second-best sense. By deterring shirking, the hungry workers hanging around the factory gates are performing a socially valuable function (but they mustn't be paid for it!). The idea of paying high wages to increase the threat of dismissal is old, and can even be found in {\it The Wealth of Nations} (Smith [1776] p. 207). What is new in Shapiro \& Stiglitz is the observation that unemployment is generated by these ``efficiency wages.'' These firms behave paradoxically. They pay workers more than necessary to attract them, and outsiders who offer to work for less are turned away. Can this explain why ``overqualified'' jobseekers are unsuccessful and mediocre managers are retained? Employers are unwilling to hire someone talented, because he could find another job after being fired for shirking, and trustworthiness matters more than talent in some jobs. This discussion should remind you of the product quality game of Section 5.4. There too, purchasers paid more than the reservation price in order to give the seller an incentive to behave properly, because a seller who misbehaved could be punished by termination of the relationship. The key characteristic of such models is that there is a constraint on the amount of contractual punishment for misbehavior and that the participation constraint is not binding in equilibrium. \subsection{ Tournaments} \noindent Games in which relative performance is important are called {\bf tournaments}. Tournaments are similar to auctions, the difference being that the actions of the losers matter directly, unlike in auctions. Like auctions, they are especially useful when the principal wants to elicit information from the agents. A principal-designed tournament is sometimes called {\bf yardstick competition} because the agents provide the measure for their wages. Farrell (unpublished) uses a tournament to explain how ``slack'' might be the major source of welfare loss from monopoly, an old idea usually prompted by faulty reasoning. The usual claim is that monopolists are inefficient because they, unlike competitive firms, do not have to maximize profits to survive. This relies on the dubious assumption that firms care about survival, not profits. Farrell makes a subtler point: although the shareholders of a monopoly maximize profit, the managers maximize their own utility, and moral hazard is severe without the benchmark of other firms' performances. Let firm Apex have two possible production techniques, $Fast$ and $Careful$. Independently for each technique, Nature chooses production cost $c=1$ with probability $\theta$ and $c=2$ with probability $1-\theta$. The manager can either choose a technique at random or investigate the costs of both techniques at a utility cost to himself of $\alpha$. The shareholders can observe the resulting production cost, but not whether the manager investigates. If they see the manager pick $Fast$ and a cost of $c=2$, they do not know whether he chose it without investigating, or investigated both techniques and found they were both costly. The wage contract is based on what the shareholders can observe, so it takes the form $(w_1,w_2)$, where $w_1$ is the wage if $c=1$ and $w_2$ if $c=2$. The manager's utility is log $w$ if he does not investigate, log $w$ $-\alpha$ if he does, and the reservation utility of log $\bar{w}$ if he quits. If the shareholders want the manager to investigate, the contract must satisfy the self selection constraint \begin{equation} \label{e4} U({\rm not\; investigate}) \leq U ({\rm investigate}). \end{equation} If the manager investigates, he still fails to find a low cost technique with probability $(1-\theta)^2$, so (8.\ref{e4}) is equivalent to \begin{equation} \label{e5} \theta {\rm log}\;w_1 + (1-\theta) {\rm log}\; w_2 \leq [1- (1-\theta)^2] {\rm log} \;w_1 + (1-\theta)^2 {\rm log} \;w_2 - \alpha. \end{equation} The self selection constraint is binding, since the shareholders want to keep the manager's compensation to a minimum. Turning inequality (8.\ref{e5}) into an equality and simplifying yields \begin{equation} \label{e6} \theta (1-\theta) {\rm log}\; \frac{w_1}{w_2} = \alpha. \end{equation} The participation constraint, which is also binding, is $ U(\bar{w}) = U ({\rm investigate})$, or \begin{equation} \label{e7} {\rm log}\; \bar{w} =[1- (1-\theta)^2] {\rm log}\; w_1 + (1-\theta)^2 {\rm log}\; w_2 - \alpha. \end{equation} Solving equations (8.\ref{e6}) and (8.\ref{e7}) together for $w_1$ and $w_2$, yields \begin{equation} \label{e8} \begin{array}{rl} w_1 = & \bar{w}e^{\alpha/\theta}.\\ w_2 = & \bar{w}e^{-\alpha/(1-\theta)}.\\ \end{array} \end{equation} The expected cost to the firm is \begin{equation} \label{e9} [1- (1-\theta)^2] \bar{w}e^{\alpha/\theta} + (1-\theta)^2 \bar{w}e^{-\alpha/(1-\theta)}. \end{equation} If the parameters are $\theta = 0.1$, $\alpha = 1$, and $\bar{w} = 1$, the rounded values are $w_1 =22,026$ and $w_2 = 0.33$, and the expected cost is $4,185$. Quite possibly, the shareholders decide it is not worth making the manager investigate. But suppose that Apex has a competitor, Brydox, in the same situation. The shareholders of Apex can threaten to boil their manager in oil if Brydox adopts a low cost technology and Apex does not. If Brydox does the same, the two managers are in a prisoner's dilemma, both wishing not to investigate, but each investigating from fear of the other. The forcing contract for Apex specifies $w_1=w_2$ to fully insure the manager, and boiling in oil if Brydox has lower costs than Apex. The contract need satisfy only the participation constraint that log $w - \alpha =$ log $\bar{w}$, so $ w = 2.72$ and the cost of learning to Apex is only $2.72$, not $4,185$. Competition raises efficiency, not through the threat of firms going bankrupt but through the threat of managers being fired. \subsection{ Institutions and Agency Problems} \noindent {\bf Ways to Alleviate Agency Problems} \noindent Usually when agents are risk averse, the first-best cannot be achieved, because some tradeoff must be made between providing the agent with incentives and keeping his compensation from varying too much between states of the world, or because it is not possible to punish him sufficiently. We have looked at a number of different ways to solve the problem, and at this point a listing might be useful. Each method is illustrated by application to the particular problem of executive compensation, which is empirically important, and interesting both because explicit incentive contracts are used and because they are not used more often (see Baker, Jensen \& Murphy [1988]). \noindent (1) {\bf Reputation} (5.3, 5.4, 6.4, 15.1) \\ Managers are promoted on the basis of past effort or truthfulness. \noindent (2) {\bf Risk-Sharing Contracts} (7.3, 7.4, 7.5 ) \\ The executive receives not only a salary, but call options on the firm's stock. If he reduces the stock value, his options fall in value. \noindent (3) {\bf Boiling in Oil} (7.4) \\ If the firm would only become unable to pay dividends if the executive shirked and was unlucky, the threat of firing him when the firm skips a dividend will keep him working hard. \noindent (4) {\bf Selling the Store} (7.4) \\ The managers buy the firm in a leveraged buyout. \noindent (5) {\bf Efficiency Wages} (8.4)\\ To make him fear losing his job, the executive is paid a higher salary than his ability warrants (cf. Rasmusen [1988b] on mutual banks). \noindent (6) {\bf Tournaments} (8.5) \\ Several vice presidents compete and the winner succeeds the president. \noindent (7) {\bf Monitoring} (3.4) \\ The directors hire a consultant to evaluate the executive's performance. \noindent (8) {\bf Repetition} \\ Managers are paid less than their marginal products for most of their career, but are rewarded later with higher salaries or generous pensions if their career record has been good. \noindent (9) {\bf Changing the Type of the Agent}\\ Older executives encourage the younger by praising ambition and hard work. We have talked about all but the last two solutions. Repetition enables the contract to come closer to the first-best if the discount rate is low (Radner [1985]). ``Production Game V'' failed to attain the first-best in Section 7.2 because output depended on both the agent's effort and random noise. If the game were repeated 50 times with independent drawings of the noise, the randomness would average out and the principal could form an accurate estimate of the agent's effort. This is really begging the question, by saying that in the long run effort can be observed after all. Changing the agent's type by increasing the direct utility from desirable or decreasing that from undesirable behavior is a solution that has received little attention from economists, who have focussed on changing the utility by changing monetary rewards. Akerlof (1983), one of the few papers on the subject of changing type, points out that the moral education of children, not just their intellectual education, affects their productivity and success. The attitude of economics, however, has been that while virtuous agents exist, the rules of an organization need to be designed with the unvirtuous agents in mind. As the Chinese thinker Han Fei said some two thousand years ago \begin{quotation} \begin{small} ``Hardly ten men of true integrity and good faith can be found today, and yet the offices of the state number in the hundreds. If they must be filled by men of integrity and good faith, then there will never be enough men to go around; and if the offices are left unfilled, then those whose business it is to govern will dwindle in numbers while disorderly men increase. Therefore the way of the enlighted ruler is to unify the laws instead of seeking for wise men, to lay down firm policies instead of longing for men of good faith.'' (Han Fei [1964], p. 109 from his chapter, ``The Five Vermin'') \end{small} \end{quotation} The number of men of true integrity has probably not increased as fast as the size of government, so Han Fei's observation remains valid, but it should be kept in mind that honest men do exist and honesty can enter into rational models. There are tradeoffs between spending to foster honesty and spending for other purposes, and there may be tradeoffs between using the second-best contracts designed for agents indifferent about the truth and using the simpler contracts appropriate for honest agents. \bigskip \noindent {\bf Government Institutions and Agency Problems} The field of law is well-suited to analysis by principal-agent models. Even in the 19th century, Holmes (1881, p. 31) conjectured in {\it The Common Law} that the reason why sailors at one time received no wages if their ship was wrecked was to discourage them from taking to the lifeboats too early to save it. The reason why such a legal rule may have been suboptimal is not that it was unfair--- presumably sailors knew the risk before they set out--- but because incentive compatibility and insurance work in opposite directions. If sailors are more risk averse than ship owners, and pecuniary advantage would not add much to their effort during storms, then the owner ought to provide insurance to the sailors by guaranteeing them wages whether the voyage succeeds or not. Another legal question is who should bear the cost of an accident: the victim (for example, a pedestrian hit by a car) or the person who caused it (the driver). The economist's answer is that it depends on who has the most severe moral hazard. If the pedestrian could have prevented the accident at the lowest cost, he should pay; otherwise, the driver. This idea of the {\bf least-cost avoider} is extremely useful in the economic analysis of law, and is a major theme of Posner's treatise on law and economics (Posner [1992]). Insurance or wealth transfer may also enter as considerations. If pedestrians are more risk averse, drivers should bear the cost, and according to some political views, if pedestrians are poorer, drivers should bear the cost. Note that this last consideration--- wealth transfer--- is not relevant to private contracts. If a principal earning zero profits is required to bear the cost of work accidents, the agent's wage will be lower than if he bore them instead. Criminal law is also concerned with tradeoffs between incentives and insurance. Holmes (1881, p. 40) also notes, approvingly, that Macaulay's draft of the Indian Penal Code made breach of contract for the carriage of passengers a criminal offense. The reason is that the palanquin-bearers were too poor to pay damages for abandoning their passengers in desolate regions, so the power of the state was needed to provide for heavier punishments than bankruptcy. In general, however, the legal rules actually used seem to diverge more from optimality in criminal law than civil law. If, for example, there is no chance that an innocent man can be convicted of embezzlement, boiling embezzlers in oil might be good policy, but most countries would not allow this. Taking the example a step further, if the evidence for murder is usually less convincing than for embezzling, our analysis could easily indicate that the penalty for murder should be less, but such reasoning offends the common notion of matching the severity of punishment with the crime. \bigskip \noindent {\bf Private Institutions and Agency Problems} While agency theory can be used to explain and perhaps improve government policy, it also helps explain the development of many curious private institutions. Agency problems are an important hindrance to economic development, and may explain a number of apparently irrational practices. Popkin (1979, pp. 66, 73, 157) notes a variety of these. In Vietnam, for example, absentee landlords were more lenient than local landlords, but improved the land less, as one would expect of principals who suffer from informational disadvantages {\it vis \`{a} vis} their agents. Along the pathways in the fields, farmers would plant early-harvesting rice that the farmer's family could harvest by itself in advance of the regular crop, so that hired labor could not grab handfuls as they travelled. In 13th-century England, beans were seldom grown, despite their nutritional advantages, because they were too easy to steal. Some villages tried to solve the problem by prohibiting anyone from entering the beanfields except during certain hours marked by the priest's ringing the church bell, so everyone could tend and watch their beans at the same official time. In less exotic settings, moral hazard provides another reason besides tax benefits why employees take some of their wages in fringe benefits. Professors are granted some of their wages in university computer time because this induces them to do more research. Having a zero marginal cost of computer time is a way around the moral hazard of slacking on research, despite being a source of moral hazard in wasting computer time. A less typical but more imaginative example is that of the bank in Minnesota which, concerned about its image, gave each employee \$100 in credit at certain clothing stores to upgrade their style of dress. By compromising between paying cash and issuing uniforms the bank could hope to raise both its profits and the utility of its employees. (``The \$100 Sounds Good, but what do they Wear on the Second Day?'' {\it Wall Street Journal}, 16 October 1987, p. 17.) Longterm contracts are an important occasion for moral hazard, since so many variables are unforeseen, and hence noncontractible. The term {\bf opportunism} has been used to describe the behavior of agents who take advantage of noncontractibility to increase their payoff at the expense of the principal (see Williamson [1975] and Tirole [1986]). Smith may be able to extract a greater payment from Jones than was agreed in their contract, because when a contract is incomplete, Smith can threaten to harm Jones in some way. This is called {\bf hold-up potential} (Klein, Crawford, \& Alchian [1978]). Hold-up potential can even make an agent introduce competing agents into the game, if competition is not so extreme as to drive rents to zero. Michael Granfield tells me that the Fairchild company once developed a new patent on a component of electronic fuel injection systems that it sought to sell to another firm, TRW. TRW offered a much higher price if Fairchild would license its patent to other producers, fearing the hold-up potential of buying from just one supplier. TRW could have tried writing a contract to prevent hold-up, but knew that it would be difficult to prespecify all the ways that Fairchild could cause harm, including not only slow delivery, poor service, and low quality, but also sins of omission like failing to sufficiently guard the plant from shutdown due to accidents and strikes. It should be clear from the variety of these examples that moral hazard is a common problem. Now that the first flurry of research on the principal-agent problem has finished, researchers are beginning to use the new theory to study institutions that were formerly relegated to descriptive ``soft'' scholarly work. \subsection { Teams} \noindent To conclude this chapter, let us switch our focus from the individual agent to a group of agents. We have already looked at tournaments, which need more than one agent to work, but a tournament still takes place in a situation where each agent's output is distinct. The tournament is a solution to the standard problem, and the principal could always fall back on other solutions such as individual risk-sharing contracts. In this section, the effect of there being a group of agents is to destroy the effectiveness of the individual risk-sharing contracts, because observed output is a joint function of the unobserved effort of many agents. Even though there is a group, a tournament is impossible, because only one output is observed. The situation has much of the flavor of ``The Civic Duty Game'' of Chapter 3: the actions of a group of players produce a joint output, and each player wishes that the others will carry out the costly actions. A teams model is defined as follows. \noindent {\it A {\bf team} is a group of agents who independently choose effort levels that result in a single output for the entire group.} We will look at teams using the following game. \begin{center} {\bf ``Teams''}\\ (Holmstrom [1982]) \end{center} {\bf Players}\\ A principal and $n$ agents. \noindent {\bf Order of Play}\\ (1) The principal offers a contract to each agent $i$ of the form $w_i(q)$, where $q$ is total output.\\ (2) The agents decide whether or not to accept the contract.\\ (3) The agents simultaneously pick effort levels $e_i$, ($i = 1,\dots,n$).\\ (4) Output is $q(e_1,\ldots e_n)$. \noindent {\bf Payoffs}\\ If any agent rejects the contract, all payoffs equal zero. Otherwise,\\ \begin{tabular}{ll} $ \pi_{principal}$ & $= q - \sum_{i=1}^n w_i$;\\ $\pi_{i}$ & $= w_i - v_i(e_i)$, where $v'_i> 0$ and $v''_i > 0$. \end{tabular} Despite the risk neutrality of the agents, ``selling the store'' fails to work here, because the team of agents still has the same problem as the employer did. The team's problem is cooperation between agents, and the principal is peripheral. \noindent Denote the efficient vector of actions by $e^*$. An efficient contract is \begin{equation} \label{e10} w_i(q) = \left\{ \begin{array}{ll} b_i& {\rm if}\; q \geq q(e^*).\\ 0 & {\rm if} \;q < q(e^*).\\ \end{array} \right. \end{equation} where $\sum_{i=1}^n b_i = q(e^*)$ and $b_i > v_i(e^*_i)$. Contract (8.\ref{e10}) gives agent $i$ the wage $b_i$ if all agents pick the efficient effort, and nothing if any of them shirks, in which case the principal keeps the output. The teams model gives one reason to have a principal: he is the residual claimant who keeps the forfeited output. Without him, it is questionable whether the agents would carry out the threat to discard the output if, say, it were 99 instead of the efficient 100. There is a problem of dynamic consistency. The agents would like to commit in advance to throw away output, but only because they never have to do so in equilibrium. If the modeller wishes to disallow discarding output, he imposes the {\bf budget-balancing} constraint that the sum of the wages equals exactly the output, no more and no less. But budget balancing creates a problem for the team that is summarized in Proposition 8.1. \noindent {\bf Proposition 8.1.} { \it If there is a budget-balancing constraint, no differentiable wage contract $w_i(q)$ generates an efficient Nash equilibrium.} \noindent {\bf Proof}\\ Agent $i$'s problem is \begin{equation}\label{e11} \stackrel{Maximize}{e_i} \;\;\; w_i(q(e)) - v_i(e_i). \end{equation} His first order condition is \begin{equation}\label{e12} \left( \frac{dw_i}{dq} \right) \left( \frac{dq}{de_i} \right) - \frac{dv_i}{de_i} = 0. \end{equation} With budget balancing and a linear utility function, the Pareto optimum maximizes the sum of utilities (something not generally true), so the optimum solves \begin{equation} \label{e13} \begin{array}{cl} Maximize & q(e) - \sum_{i=1}^n v_i(e_i)\\ e_1,\ldots, e_n & \\ \end{array} \end{equation} The first order condition is that the marginal dollar contribution to output equal the marginal disutility of effort: \begin{equation} \label{e14} \frac{dq}{d{e_i}} - \frac{d{v_i}}{d{e_i}} = 0. \end{equation} Equation (8.\ref{e14}) contradicts (8.\ref{e12}), the agent's first order condition, because $\frac{dw_i}{dq}$ is not equal to one. If it were, agent $i$ would be the residual claimant and receive the entire marginal increase in output--- but under budget balancing, not every agent can do that. Because each agent bears the entire burden of his marginal effort and only part of the benefit, the contract does not achieve the first-best. Without budget balancing, on the other hand, if the agent shirked a little he would gain the entire leisure benefit from shirking, but he would lose his entire wage under the optimal contract. \noindent {\bf Discontinuities in Public Good Payoffs} \noindent Ordinarily, there is a free rider problem if several players each pick a level of effort which increases the level of some public good whose benefits they share. Noncooperatively, they choose effort levels lower than if they could make binding promises. Mathematically, let identical risk-neutral players indexed by $i$ choose effort levels $e_i$ to produce amount $q(e_1,\ldots,e_n$) of the public good, where $q$ is a continuous function. Player $i$'s problem is \begin{equation} \label{e15} \stackrel{Maximize}{e_i} q(e_1,\ldots,e_n) - e_i, \end{equation} which has first order condition \begin{equation} \label{e16} \frac{\partial q}{\partial e_i} - 1 = 0, \end{equation} whereas the greater, first-best effort $n$-vector $e^*$ is characterized by \begin{equation} \label{e17} \sum_{i=1}^n \frac{\partial q}{\partial e_i} - 1 = 0. \end{equation} If the function $q$ is discontinuous at $e^*$ (for example, $q=0$ if $e_i < e^*_i$ for any $i$), the strategy profile $e^*$ can be a Nash equilibrium. In ``Teams'' the same effect is at work. Although the ``Teams'' function is not discontinuous, contract (8.10) is constructed to obtain the same incentives as if it were. The first-best can be achieved because the discontinuity at $e^*$ makes every player the marginal, decisive player: if he shirks a little, output falls drastically and with certainty. Either of two modifications restores the free rider problem and induces shirking: \noindent (1) Let $q$ be a function not only of effort but of random noise--- Nature moves after the players. Uncertainty makes the {\it expected} output a continuous function of effort.\\ (2) Let players have incomplete information about the critical value---Nature moves before the players and chooses $e^*$. Incomplete information makes the {\it estimated} output a continuous function of effort. The discontinuity phenomenon is common. Examples, not all of which note the problem, include: \noindent (1) Effort in teams (Holmstrom [1982], Rasmusen [1987]).\\ (2) Entry deterrence by an oligopoly (Bernheim [1984], Waldman [1987]). \\ (3) Output in oligopolies with trigger strategies (Porter [1983a]).\\ (4) Patent races (Section 14.1).\\ (5) Tendering shares in a takeover (Grossman \& Hart [1980], Section 13.5).\\ (6) Preferences for levels of a public good. \begin{small} \bigskip \noindent {\bf NOTES} \noindent {\bf N8.1} {\bf Pooling vs. Separating Equilibrium, and the Revelation Principle} \begin{itemize} \item The books by Fudenberg \& Tirole (1991a), Laffont \& Tirole (1993), and Spulber (1989), and Baron's chapter in the {\it Handbook of Industrial Organization} edited by Schmalensee and Willig are good places to look for more on mechanism design. \item Levmore (1982) discusses hidden knowledge problems in tort damages, corporate freezeouts, and property taxes in a law review article. \item In moral hazard with hidden knowledge, the contract must ordinarily satisfy only one participation constraint, whereas in adverse selection problems there is a different participation constraint for each type of agent. An exception is if there are constraints limiting how much an agent can be punished in different states of the world. If, for example, there are bankruptcy constraints, then if the agent has different wealths across the $N$ possible states of the world, there will be $N$ constraints for how negative his wage can be, in addition to the one participation constraint. These can be looked at as {\bf interim } participation constraints, since they represent the idea that the agent wants to get out of the contract once he observes the state of the world midway through the game. \item The revelation principle was named by Myerson [1979] and can be traced back to Gibbard (1973). A further reference is Dasgupta, Hammond \& Maskin (1979). Myerson's game theory book is, as one might expect, a good place to look for further details (Myerson [1991, pp. 258-63, 294-99]). \item Moral hazard frequently occurs in public policy. Should the doctors who prescribe drugs also be allowed to sell them? The question trades off the likelihood of overprescription against the potentially lower cost and greater convenience of doctor-dispensed drugs. See ``Doctors as Druggists: Good Rx for Consumers?'' {\it Wall Street Journal}, 25 June 1987, p. 24. \item For a careful discussion of the unravelling argument for information revelation, see Milgrom (1981b). \item A hidden knowledge game requires that the state of the world matter to one of the players' payoffs, but not necessarily in the same way as in ``Production Game VI''. ``The Salesman Game'' of Section 8.2 effectively uses the utility function $U(e,w,\theta)$ for the agent and $V(q-w)$ for the principal. The state of the world matters because the agent's disutility of effort varies across states. In other problems, his utility of money might vary across states. \end{itemize} \bigskip \noindent {\bf N8.2} { \bf An Example of Moral Hazard with Hidden Knowledge: ``The Salesman Game''} \begin{itemize} \item Sometimes students know more about their class rankings than the professor does. One professor of labor economics used a mechanism of the following kind for grading class discussion. Each student $i$ reports a number evaluating other students in the class. Student $i$'s grade is an increasing function of the evaluations given $i$ by other students and of the correlation between $i$'s evaluations and the other students'. There are many Nash equilibria, but telling the truth is a focal point. \item In dynamic games of moral hazard with hidden knowledge the {\bf ratchet effect} is important: the agent takes into account that his information-revealing choice of contract this period will affect the principal's offerings next period. A principal might allow high prices to a public utility in the first period to discover that its costs are lower than expected, but in the next period the prices would be lowered. The contract is ratcheted irreversibly to be more severe. Hence, the company might not choose a contract which reveals its costs in the first period. This is modelled in Freixas, Guesnerie \& Tirole (1985) $\;\;\;$ Baron (1989) notes that the principal might purposely design the equilibrium to be pooling in the first period so self selection does not occur. Having learned nothing, he can offer a more effective separating contract in the second period. \item We can only find weak Nash equilibria for most hidden knowledge models, because many contracts can achieve the same outcome by specifying different out-of-equilibrium punishments. In the context of ``The Salesman Game'', the contract could specify either ($w=w_2$ if $q > q_2$) or ($w =0$ for $q > q_2$). The salesman would choose $q = q_2$ in either case. \end{itemize} \bigskip \noindent {\bf N8.4} { \bf Efficiency Wages} \begin{itemize} \item For surveys of the efficiency wage literature, see the article by L. Katz (1986), the book of articles edited by Akerlof \& Yellen (1986), and the book-length survey by Weiss (1990). \item While the efficiency wage model does explain involuntary unemployment, it does not explain cyclical changes in unemployment. \item The efficiency wage idea is based on the same idea as the Klein \& Leffler (1981) model of product quality formalized in Section 5.3. If no punishment is available for player who is tempted to misbehave, a punishment can be created by giving him something to take away. This something can be a high-paying job or a loyal customer. It is also similar to the idea familiar in politics and university administration of {\bf co-opting} opponents. To tame the radical student association, give them an office of their own which can be taken away if they seize the dean's office. Yet another field of application is moral hazard with hidden knowledge; Rasmusen (1988b) shows yet another context: when depositors do not know which investments are risky and which are safe, mutual bank managers can be highly paid to deter them from making risky investments that might cost them their jobs (see the article for details on what happened after 1980). \item Adverse selection can also drive an efficiency wage model. We will see in Chapter 9 that a customer might be willing to pay a high price to attract sellers of high-quality cars when he cannot detect quality directly. \end{itemize} \bigskip \noindent {\bf N8.5} { \bf Tournaments} \begin{itemize} \item An article which stimulated much interest in tournaments is Lazear \& Rosen (1981), which discusses in detail the importance of risk aversion and adverse selection. \item One example of a tournament is the two-year, three-man contest in which to choose its new chairman Citicorp named three candidates as vice-chairmen: the head of consumer banking, the head of corporate banking, and the legal counsel. Earnings reports were even split into three components, two of which were the corporate and consumer banking (the third was the ``investment'' bank, irrelevant to the tournament). See ``What Made Reed Wriston's Choice at Citicorp,'' {\it Business Week}, 2 July 1984, p. 25. \item General Motors has tried a tournament among its production workers. During a depressed year, management credibly threatened to close down the auto plant with the lowest productivity. Reportedly, this did raise productivity. Such a tournament is interesting because it helps explain why a firm's supply curve could be upward sloping even if all its plants are identical, and why it might hold excess capacity. Should information on a plant's current performance have been released to other plants? See ``Unions Say Auto Firms Use Interplant Rivalry to Raise Work Quotas,'' {\it Wall Street Journal}, 8 November 1983, p. 1. \item Under adverse selection, tournaments must be used differently than under moral hazard because agents cannot control their effort. Instead, tournaments are used to deter agents from accepting contracts in which they must compete for a prize with other agents of higher ability. \item Interfirm management tournaments run into difficulties when shareholders want managers to cooperate in some arenas. If managers collude in setting prices, for example, they can also collude to make life easier for each other. \item Antle \& Smith (1986) is an empirical study of tournaments in managers' compensation. Rosen (1986) is a theoretical model of a labor tournament in which the prize is promotion. \item Suppose a firm conducts a tournament in which the best-performing of its vice-presidents becomes the next president. Should the firm fire the most talented vice-president before it starts the tournament? The answer is not obvious. Maybe in the tournament's equilibrium, Mr Talent works less hard because of his initial advantage, so that all of the vice-presidents retain the incentive to work hard. \item A tournament can reward the winner, or shoot the loser. Which is better? Nalebuff \& Stiglitz (1983) say to shoot the loser, and Rasmusen (1987) finds a similar result for teams, but for a different reason. Nalebuff \& Stiglitz's result depends on uncertainty and a large number of agents in the tournament, while Rasmusen's depends on risk aversion. If a utility function is concave because the agent is risk averse, the agent is hurt more by losing a given sum than he would benefit by gaining it. Hence, for incentive purposes the carrot is inferior to the stick, a result unfortunate for efficiency since penalties are often bounded by bankruptcy or legal constraints. \item Using a tournament, the equilibrium effort might be greater in a second-best contract than in the first-best, even though the second-best is contrived to get around the problem of inducing sufficient effort. Also, a pure tournament, in which the prizes are distributed solely according to the ordinal ranking of output by the agents, is often inferior to a tournament in which an agent must achieve a significant margin of superiority over his fellows in order to win (Nalebuff \& Stiglitz [1983]). Companies using sales tournaments sometimes have prizes for record yearly sales besides ordinary prizes, and some long distance athletic races have non-ordinal prizes to avoid dull events in which the best racers run ``tactical races.'' \item Organizational slack of the kind described in the Farrell model has important practical implications. In dealing with bureaucrats, one must keep in mind that they are usually less concerned with the organization's prosperity than with their own. In complaining about bureaucratic ineptitude, it may be much more useful to name particular bureaucrats and send them copies of the complaint than to stick to the abstract issues at hand. Private firms, at least, are well aware that customers help monitor agents. \end{itemize} \bigskip \noindent {\bf N8.6} { \bf Institutions and Agency Problems} \begin{itemize} \item Gaver \& Zimmerman (1977) describes how a performance bond of 100 percent was required for contractors building the BART subway system in San Francisco. ``Surety companies'' generally bond a contractor for five to 20 times his net worth, at a charge of 0.6 percent of the bond per year, and absorption of their bonding capacity is a serious concern for contractors in accepting jobs. \item Even if a product's quality need not meet government standards, the seller may wish to bind himself to them voluntarily. Stroh's {\it Erlanger} beer proudly announces on every bottle that although it is American, ``Erlanger is a special beer brewed to meet the stringent requirements of Reinheitsgebot, a German brewing purity law established in 1516.'' Inspection of household electrical appliances by an independent lab to get the ``$U_L$'' listing is a similarly voluntary adherence to standards. \item The stock price is a way of using outside analysts to monitor an executive's performance. When General Motors bought EDS, they created a special class of stock, GM-E, which varied with EDS performance and could be used to monitor it. \end{itemize} \bigskip \noindent {\bf N8.7} {\bf Teams } \begin{itemize} \item {\bf Team theory}, as developed by Marschak \& Radner (1972) is an older mathematical approach to organization. In the old usage of ``team'' (different from the current, Holmstrom [1982] usage), several agents who have different information but cannot communicate it must pick decision rules. The payoff is the same for each agent, and their problem is coordination, not motivation. \item The efficient contract (8.\ref{e10}) supports the efficient Nash equilibrium, but it also supports a continuum of inefficient Nash equilibria. Suppose that in the efficient equilibrium all workers work equally hard. Another Nash equilibrium is for one worker to do no work and the others to work inefficiently hard to make up for him. \item {\bf A Teams contract with hidden knowledge.} In the 1920s, National City Co. assigned 20 percent of profits to compensate management as a group. A management committee decided how to share it, after each officer submitted an unsigned ballot suggesting the share of the fund that Chairman Mitchell should have, and a signed ballot giving his estimate of the worth of each of the other eligible officers, himself excluded. (Galbraith [1954] p. 157) \item {\bf A First-Best, Budget-Balancing Contract when Agents are Risk Averse} Proposition 8.1 can be shown to hold for any contract, not just for differentiable sharing rules, but it does depend on risk neutrality and separability of the utility function. Consider the following contract from Rasmusen (1987):\\ \begin{equation}\label{e21} w_i = \left\{ \begin{array}{ll} b_i& {\rm if}\; q \geq q(e^*).\\ 0& {\rm with\; probability}\; (n-1)/n \;{\rm if}\; q < q(e^*),\\ q& {\rm with\; probability}\; 1/n \;{\rm if}\; q < q(e^*).\\ \end{array} \right. \end{equation} If the worker shirks, he enters a lottery. If his risk aversion is strong enough, he prefers the certain return $b_i$, so he does not shirk. If agents' wealth is unlimited, then for any positive risk aversion we could construct such a contract, by making the losers in the lottery accept negative pay. \item A teams contract like (8.\ref{e10}) is not a tournament. Only absolute performance matters, even though the level of absolute performance depends on what all the players do. \item {\bf The budget-balancing constraint.} The legal doctrine of ``consideration'' makes it difficult to make binding, Pareto-suboptimal promises. An agreement is not a legal contract unless it is more than a promise: both parties have to receive something valuable for the courts to enforce the agreement. \item Adverse selection can be incorporated into a teams model. A team of workers who may differ in ability produce a joint output, and the principal tries to ensure that only high-ability workers join the team. See Rasmusen \& Zenger (1990). \end{itemize} \end{document}