by Filip Palda
As if adverse selection were not a sufficiently daunting challenge to social organizations, a further problem known as “moral hazard” follows upon admission to the organization. Even if a separating equilibrium exists in which low-risk people pool uniquely with each other for insurance, they might be tempted to be lax about taking risks, or might even take risks on purpose in order to profit from some important payout.
Consider insurance and the old joke of the farmer who tells his friend he has just bought crop insurance against fire and hail. The friend scratches his head and says, “Well, I understand about the fire insurance, but how do you make it hail?” The point is that for insurance in which people cannot influence the outcome, moral hazard is not a problem for either the insured or insurers.
A wedge of suspicion slips between the two in cases where the insured party controls what theorists call a “self-protection variable”, meaning the ability to take precautions that minimize risk or to expose themselves to needless risk. Suspicion and obfuscation can arise when the self-protection variable is difficult for the insurer to observe. Then the prospect of manipulating this variable for their own gain acts as a hazard to the morals of those buying insurance.
Armen Alchian and Harold Demsetz (1972) showed that moral hazard is not just a problem for insurance markets but also for companies. Once they have passed through the filters of the hiring process, even highly qualified and talented managers may decide to “free-ride” on the efforts of others. When such free-riding becomes endemic, as it seemed to be in East Bloc countries at the end of the 1980s, an entire system of social organization may collapse.
Whereas adverse selection arises from the individual misrepresenting his or her risk type or skills, moral hazard arises from the difficulty of observing the individual’s manipulation of his or her self-protection variable. Thus both adverse selection and moral hazard are problems of information that individuals withhold to the detriment of the group. These problems arise from an asymmetry of information. Wherever such an asymmetry exists, so does the possibility of a Bayesian game.
The Spence Signal
AMONG THE FIRST to notice that Bayesian games and adverse selection were a fit, was future Nobellist Michael Spence in 1973. How do businesses know whom to hire and how much to pay? If businesses could properly assess the contribution of an employee to the bottom line, then the business could easily pay less to the less productive worker. The problem is that it can be very hard to know how much employee number 32,715 has contributed to the value of a complex output such as a jet plane. In the absence of a clear metric of performance, companies may remunerate workers based on their abilities. Often they judge these abilities by the certificates of qualification workers acquire before they enter the market. The problem businesses encounter by using this technique is that official qualifications are an imperfect, or noisy, signal of worker aptitude. Despite this difficulty it is imperative for companies to pay according to some reliable metric of worker contribution to output. And it may even be possible for the payment to elicit from workers a clear signal about their potential contributions to output!
To understand this imperative, consider a team of employees devising a new braking system for a luxury automobile. If the sum of salaries reflects the value the team of workers contributes to a company, then a policy of equal pay to workers making unequal contributions can provoke unrest among the achievers. The policy of equal pay is a clear transfer of money from achievers to non-achievers. This zero-sum burden may incite competent workers to leave the company in search of employment where they do not have to carry incompetents on their backs. As competent workers flee, fewer competent workers are left. The burden of the incompetents on them increases, and soon a mass exodus may lead to the firm’s collapse. The risk that these free-riders pose is acute because they impose zero-sum costs on their fellow workers. Their gain comes strictly at the loss of others. In the end, bad workers chase out the good ones. The challenge to the firm lies in getting workers to themselves reveal to it their abilities.
Spence’s achievement was to provide a rigorous example of a case in which employers could use their compensation strategies to elicit honest revelation from workers. He postulated a Bayesian game between the firm in a competitive job market and the potential workers it must choose from. The reward is the salary the firm chooses to pay based on education. The game is Bayesian because only the worker knows if he or she is competent or incompetent, whereas the firm knows only the general proportion of worker types in the economy. If fifty per cent of workers are known to be competent, the firm might just take its chances, engage the worker, and pay the high salary. But the firm would like to do better. It would like to somehow separate the two types. In this, its interests are aligned with competent workers who want to be believed about their type, and opposed by the incompetents who wish to misrepresent themselves.
There might be some way of having the truth come out if the competent worker could send a credible “signal” to the firm of his or her type. The firm knows that in general, fifty percent of workers are competent. Then upon observing a credible signal, the firm would increase its perceived probability that the worker is competent to perhaps sixty per cent. This credible signal would lead the firm to offer potential workers who send it a higher wage. An even more credible signal would lead to an even higher wage. But what would lead to a completely credible signal, one that contains full information about the types?
For a signal to be credible, it must be costly to send, and the competent potential hire must have lower costs of sending it than the incompetent one. Talk cannot be cheap. The firm must be careful not to set the wage for strong signals too high or the incompetent worker could be induced to bear the extra costs of sending the signal in order to get the job. Recall Muceus Scaevola, a Roman who snuck into the enemy Etruscan camp to assassinate its leadership. He bumbled, was caught, and in defiance of his captors held his right hand over a flame until it caught fire, all the while extolling Roman virtues and his defiance of the Etruscans. So impressed were the Etruscans by his bravery that they set him free. Because there was no anticipated reward in sight, Muceus’ gesture was a costly and credible signal. But if instead he had been promised his freedom and a bag of gold then the motives for his bravery might have been questioned. The inept job candidate who sees great qualifications may be moved to great efforts to attain them, perhaps through bribery, if the salary is right. What ideally happens is that the employer sets a wage premium for the better job only just high enough to make it profitable for the able worker to send the signal but not for the inept worker.
The result is a Bayesian equilibrium because the employer does not know worker types but only their spread in the economy. As Spence explained “… an equilibrium can be thought of as a set of employer beliefs that generate offered wage schedules, applicant signalling decisions, hiring, and ultimately new market data over time that are consistent with the initial beliefs” (1973, p. 360). The signal Spence had in mind was education. In his view, education could help employers separate competent from incompetent workers, even if the education had contributed nothing to the student’s abilities and knowledge. If all workers recognize that getting a degree will help them land a job, but it costs competent workers less time to get a BA than it costs incompetent workers, then given the right spread of wages, the degree would separate the two groups and serve as a perfect signal for competence.
Take, for example Isolde who is a competent potential job candidate and can do her weekly studies twice as fast as Tristan, who is an incompetent potential candidate. This means that over her years at university, Isolde can work more hours part-time earning money, and thus reduce more than Tristan the foregone income from not working full-time over the course of her education. These foregone wages are the opportunity cost of an education. If the salary difference between competent and incompetent candidates is $20,000 over the career, and Isolde’s opportunity cost of education is $19,000, then she
goes to university. If Tristan’s opportunity cost is $21,000, he does not go to university. All the Tristans and Isoldes in the economy reason this way and thus there exists a “separating equilibrium” wage which sorts high skill workers into firms that need them and shuttles low skill workers into low skill jobs. It remains for the firm to divine this wage, perhaps through trial and error as Spence suggests, though the actual process is secondary to the game-theoretic solution of this problem.
This example is almost trivial because it makes no direct use of the firm’s knowledge of the proportion of worker types in the economy. If incompetent workers had varied in their opportunity costs of getting an education, a simple separating wage might not have been obtained. Instead some incompetents at the low range of education costs of their type might have completed their BAs and so slipped into the firm. In this case fuller use of the Harsanyi solution concept for Bayesian games would come into full play because this concept was designed to apply to a spectrum of player types. This game also may have no solution if the costs of education are very high and the differences in abilities of Isolde and Tristan are small. In that case, the cost of the signal is large and potentially discouraging, especially if there is little by way of differences in education costs to distinguish the two candidates.
It is difficult to emphasize what an important turning point in game theory Spence’s analysis was. The signalling game differed from the games that had preoccupied earlier theorists because in it one or more players can control the rewards. In the stag hunt and Sherlock Holmes games, the rewards were given and players had only their choice of a move or a probability to work with. The signalling game is often much easier to solve than those other games because one or more players has the freedom to alter the conditions of the game until the best possible solution for each appears. In the case of education, the potential worker can decide how much to invest in education. This affects his costs and potential rewards. The firm decides how to vary the wage to elicit the desired signal. The reason Spence got his Nobel prize for writing one significant article in economics was because he showed that information theory and game theory could be united in a way that did away with lying in equilibrium. He was a pioneer of reverse game theory.
The signalling game also differed from previous research in that it actually had something to say about public policy. After three decades of arid theorizing some practical result was a development that came as a welcome relief to applied economists. If it were true that education had a strong signalling function, say at the university level, how should this guide government funding for undergraduates? The traditional economic argument had been that markets fail to appreciate the “externalities” or “spillovers” that an educated person generates on his or her path through life. Spillovers might be participation on hospital boards, organizing food aid, and civic spirit. Some argued that these positive manifestations should be more frequent in the person whose sensibilities had been trained up in places of “higher” learning. Even if education cost more than the amount by which it increased job productivity, the extra value of these spillovers to society would justify the government subsidy.
Spence’s signalling game raised a contrary point. If government lowered the cost of an education through subsidized tuition and generous bursaries, then incompetent potential employees might start to think it was worthwhile to get an education. As they left the ranks of academe clutching their degrees, they would march onto the job market where they would elbow out some of the more competent workers and spend years mooching off the efforts of their fellow workers. Some indication that the signal from an undergraduate education had indeed been corrupted by “degree inflation” was the search for a remedy in the rapid spread of professional schools offering professional degrees for graduates. Degrees such as the MBA were not subsidized and because they would then attract only those truly interested in investing in demonstrating their competence might serve as an appropriate signal for generating separating wages.
So where did Spence’s analysis fit in a broader picture?
Spence had suggested a means by which the deception inherent in Bayesian games could be eliminated. In his signalling game, revelation came about by the choice a potential employee made to invest his or her time and money in an education. Because the cost of education is related to the competence of the person, education would then serve as a credible signal of the student’s likelihood of turning out to be a competent employee. It is up to the firm to elicit this signal by controlling the rewards to investing in education, namely, the salary. The way to short-circuit the game lies in paying the correct salary to elicit the correct signal.
There are other games of asymmetric information where one player, usually called “the principal”, cannot tell if the signal is true, and where the other player or players, called the “agents”, have no means by which to send a credible signal. The idea in these games is to elicit the truth from people by setting up the rewards of the game in such a way that it makes truth-telling the most profitable action. Instead of investing money to elicit a signal, money is invested to elicit truthful behavior.
The Vickrey auction
THE TRICK FOR doing this was first noticed in 1961 by William Vickrey. He is credited with discovering how to elicit the truth from a few non-competitive suppliers trying to sell services to a government marketing agency at exaggerated prices. What Vickrey had in mind was some government marketing agency that wanted to buy from different suppliers and resell to consumers in such as way as to mimic what a free market would do.
Government presumably feels the need to intervene for fear that suppliers would organize themselves into a cartel to artificially boost prices. In this role as middle person, government is subject to the potential lies of suppliers complaining they need a high price because of supposedly high costs. On the other end of matters, consumers may pretend that their willingness to pay for the product is lower than it really is. The example seems contrived in the present age, where government has curtailed its direct role in managing private markets, but as we shall see, Vickery’s idea is widely applicable to many other forms of government intervention. How exactly does the truth-revelation scheme work? Let us speak of firms. The idea is similar for consumers.
First, let us consider a non-Vickrey solution to this problem and see where it goes wrong. That will better help us to understand Vickrey’s insight. In deciding what a reasonable bid is, the government does not know the individual cost of any particular firm, but may have some general idea of the proportion of firms with high and low costs. Using this “prior” information it could play the Bayesian game by developing some notion of the probability that a firm is telling the truth, given the known distribution of firm costs in the economy. The government could decide whether to believe and award the contract, not believe and exclude the firm, or to randomize by flipping a coin to determine which firm or firms get the contract. The problem is that the resulting equilibria might satisfy the Nash condition, but could be quite bad if, by randomization, government chose the high-cost firms exclusively.
Vickrey saw that government could do better by avoiding randomization and game-playing. It could neutralize the game by manipulating its conditions so as to get full revelation of cost information by firms. The term used in his day was “anti-speculation”. The modern term for this sort of reverse-game is “mechanism design”. Thinking of a truth revelation scheme Vickrey noted that, “one method, though an expensive one … [is] to arrange to purchase the commodity from suppliers and to sell it to purchasers on terms that are dependent on the reported supply and demand curves in such a way that the suppliers and purchasers will maximize their profits, individually at least, by reporting correctly, so that any misrepresentation will subject them to risk of loss” (1961, 10).
One way to make firms tell the truth is to make them aware of the cost of lying. To do this Vickrey suggested government ask them all to submit information on their production costs (which is th
e same thing as a supply curve in a competitive market). The government has no way of telling now or in the future if these costs are real or fictitious. What the government can do is tell one supplier, call it Baal Telephone, that it will consider as truthful the reports of all other suppliers. Government will then calculate on the basis of these presumably true-cost reports from the other firms what their free-market level of production should be. Then it will look at Baal Telephone’s supply report and calculate how much extra free-market production that would merit. Recall that the government is trying to calculate the optimum free market level of production by all firms. This optimum involves contracting to firms with the lowest costs the greatest amount of production.
In addition, for this extra production, government will pay to Baal the premium that consumers would have been willing to pay for it over the free-market price. The idea here is that consumers seldom pay exactly what they were willing to pay. Often the price they pay is below their maximum holdout price. So now Baal must consider that if it pretends costs are too large, government will calculate that its production should be small and Baal will lose out on collecting juicy consumer premiums in the form of government handouts. If Baal low-balls its costs, it will be ordered to produce beyond what consumers are willing to pay and falling into this negative zone will curtail its profits as well.
