Auctions have been used for more than 2,500 years to allocate a single indivisible asset. They are also used to sell multiple units of some commodities, such as rare wine or a new crop of tulip bulbs. There are many different types of auctions in use, and far more that have never been tried but could be employed if we felt that they served some purpose. The aim of this chapter is to determine which type of auction should be used in a particular situation. Accordingly, we need to determine which bidder would get the asset that is up for sale and then howmuch would be paid for it.

INTRODUCTION

When the government sells things at auction – treasury bills, oil-drilling rights, or a TV broadcast frequency, for instance – the appropriate criterion for determining which type of auction should be used is the maximization of general consumer welfare. Because the bidders are usually firms, we recommend the auction type that would put the asset in the hands of the firm that would use it to produce the highest level of consumer welfare. Fortunately, this is correlated with the value of the asset to a bidder: the more valuable the asset is to consumers when it is used by firm X, themore profit X anticipates from owning the asset, and thus the higher the value that X itself places on the asset. (Section 6.1.2 explains why revenue net of cost is a good measure of the benefit that consumers derive from a firm's activities.) The discounted stream of profits that would flow from the asset is the individual firm's reservation value, and it is a hidden characteristic. If the government were to ask each firm to report its reservation value and awarded the asset to the high-value firm it would get nothing resembling truthful revelation. Each would have a strong incentive to overstate the value it places on the asset in an attempt to increase the probability of being awarded the asset.

This chapter investigates preference revelation in a standard economicmodel. There is a commodity that can be consumed jointly and simultaneously by the entire community – a fireworks display, for instance. To produce this public good, resources have to be diverted from the production of commodities for private consumption. In ourmodel, as in the real world, efficiency requires a positive amount of some public good to be produced. But there is a point beyond which an increase in the supply of the public good leads to an inefficient outcome. Clearly, identification of an efficient outcome depends on individuals revealing their preferences. In this context truthful revelation of individual preference is problematic because one can consume the public good without contributing to the financing of it.

More generally, agent A's action generates a positive spillover if some other agent B directly benefits as a result of that action. For example, if A removes weeds from his own property, then neighbor B's grass will have fewer weeds because one source of seed has been eliminated. In this case, most of the benefit of A's effort is reaped by A, so we say that the spillover is incomplete. However, if C produces a fireworks display then everyone else in town will have just as good a view of it as C and hence the spillover is complete. When the agent creating the spillover benefit is not compensated for the positive effect on the welfare of others, we refer to it as an externality. Important examples include the containment of a virulent disease by a health organization, the retardation of global warming or ozone depletion by international treaty, and publication of information concerning public safety.

Our aim is to provide the individual decision maker with incentive to consider the benefit that others derive from his or her actions. The decision maker can be a single individual or household, or a region within a country, or even a country itself. When one country takes costly measures to reduce its output of carbon dioxide any resulting retardation of global warming is a benefit that is captured by every country.

This chapter and the next four investigate hidden characteristic problems, from voting to used-car markets to kidney exchanges. In some cases market forces have fostered contracts and other devices that induce agents to reveal their hidden characteristics. This does not mean that the equilibrium outcome is efficient in each case, however. There are incentive schemes that do induce truthful revelation of the hidden information while at the same time bringing the system close to efficiency – the Vickrey auction of Chapter 6 for instance.

Markets can be very creative in circumventing hidden information problems – for instance, warranties on consumer durables. The producer of a shoddy appliance cannot afford to offer a substantial warranty: the point of producing a low-quality item is to get more profit by keeping costs down, but if appliances are being returned for replacement or repair then costs will be high, not low. A producer who deliberately sets out to profit by misleading consumers about the quality of the product will not be able to offer the same kind of warranty as the producer of a high-quality product. The latter is credibly signaling high quality to the consumer by offering a substantial warranty. Reputable manufacturers often make good on a warranty even after it has expired, as long as the appliance is returned a month or less after the expiration date.

Although not always delivering an efficient outcome, the market system often goes a long way toward eliciting the hidden information. The next section begins with a standard example of the hidden characteristic phenomenon.

Networks can be tiny – your circle of very close friends, for instance. They can be vast, as in the case of the individuals and institutions connected to you and to each other through the world wide web. The internet has not only given us an extraordinary increase in the number of sources from which we can obtain information. It has also increased the value of that information, in part because of the great increase in the number of sources of information available to the compilers of any web site that you visit. (Of course, the web has also greatly increased the number of sources of misinformation.) Until the arrival of the internet, an increase in the number of sources of information brought with it a substantial increase in the cost of widespread comparison shopping: one had to sacrifice a significant amount of time to visit rival retailers. By contrast, the web has vastly reduced the cost of acquiring information from any one source, and thus has made it possible to comparison shop extensively at almost no cost. (Transactions involving rare books have increased more than a hundred-fold since the advent of the internet, because search costs have virtually dropped to zero. In the previous century collectors of rare books had to wait for the arrival of annual catalogues. These catalogues were costly and infrequently updated because of the cost and the time commitment required of their compilers.)

The internet may be the network that comes to mind first, but it is probably not the most important one. That is obviously the case in parts of the third world where there is no access to the web. Instead, networks that rely on information transmission by word-of-mouth are used to locate sources of safe drinking water, to provide access to birth control information, and for AIDS prevention campaigns, to name but a few crucial examples.

This chapter examines allocation problems for which the desired “commodities”, such as dormitory rooms, are only available in discrete units and each “consumer” wants one unit and only one unit. Moreover, allocating a desired object to the highest bidder is unacceptable, as it would be in the case of an offer of admission to a good university. The objective is to match each student with a room (or a university), or available kidneys with the patients on a transplant waiting list, and so forth.

Suppose that an economics department has a given number of students (i.e., majors) and professors, and the objective is to assign each student a professoradvisor. In this case both sides of the match have preferences: students like some professors better than others, and the professors can rank the students. There are problems for which only one side of the match has preferences: students have preferences for dormitory rooms, but the rooms don't have preferences for students.

We can also classify matching problems according to whether we can have outcomes at which an agent is paired with more than one agent of the opposite type, as in the case of college admissions. Each student is placed with only one college, but each college admits many students. Both types have preferences: each student can rank the colleges, and the colleges have preferences for students – if only for students with high test scores.

The first allocation problem that we study is a marriage model, for which there are two types of agents: there is a set ofWtypes and a set ofMtypes. Each member of each type has a preference ordering for the members of the other type, and each agent is matched with at most one member of the other type. The problem of matching students and advisors can be a marriage model. A student will have at most only one advisor, and if there is a department rule limiting a professor to at most one advisee then we have a marriage model. Our objective is not to classify allocation problems, however, but to solve them by designing satisfactory allocation procedures.

This chapter takes an economy-wide perspective and seeks a mechanism that elicits private information about individual preferences and firm production recipes to deliver an efficient allocation of private goods and services. We assume away all other hidden information problems. In particular, every consumer is assumed to know the quality of every firm's output, every employer knows the abilities of every prospective employee, every lender knows the probability of default of every creditor, and so on. Every manager can be relied on to maximize profit. In fact there is no shirking by anyone.

The economy faces an impressive challenge – to induce truthful revelation of the remaining hidden information, specifically preferences and production functions. In fact, three of the five sections even assume away this hidden information problem, highlighting instead the transmission of information. Recall that an outcome is efficient if there is no other arrangement of production and consumption activities that makes one person better off without lowering the utility of anyone else. Identification of an efficient outcome would seem to require an enormous amount of information about all of the private characteristics. Therefore, even with most of the hidden information problems assumed away, identification of an efficient outcome by the market system is a remarkable accomplishment. Social cost pricing is the key.

In a private ownership market economy the consumer maximizes utility subject to a budget constraint, and this results in a chosen consumption plan at which the marginal rate of substitution (MRS) for each pair of commodities equals the price ratio for those goods. Therefore, the price ratio transmits information about one consumer's MRS to every other consumer and every firm. The budget constraint gives consumers the incentive to employ that information in their utility maximization calculations, as Section 11.1.4 demonstrates. Profit maximization by a firm in a competitive environment results in the equilibrium price of a commodity that is also equal to the marginal cost of producing that good. Therefore, prices transmit marginal information about consumer preferences and firm production recipes.

In spite of the fact that prices transmit only marginal information, we demonstrate in Sections 11.2 and 11.3 that this allows an efficient outcome to be identified in a wide range of circumstances.

My greatest debt is to Emily Martell, an undergraduate at William and Mary. She was my research assistant for the last eight months of work on the book. Her love of learning, her ability to write good prose, and her extraordinary intellect redounded to my great benefit and to the benefit of anyone who reads this book. Emily contributed to a few of the topics – the Enron debacle among them – and read the new network chapter and some others, each with great care. She responded to requests for help with alacrity and skill. Both her research and her critique of the manuscript were exemplary. She not only identified glitches, she drew my attention to passages that were not sufficiently clear. (“Glitch” is an understatement. She saved me from a horrible blunder in Chapter 4.) Emily even corrected my prose. I am deeply grateful for her help, and blessed to have had her as a colleague. Any defects that remain can be put down to the fact that I did not give her enough time to read the entire manuscript.

I am also thankful for the input of Steven Williams of the Department of Economics, University of Illinois, Lauren Merrill of the Boston Consulting Group, and my longtime colleague Jerry Kelly.

Over the last eight years I have benefitted from the excellent research assistance of Jennifer Boardman, Anthony Guth, Sarah Turner, and Gefoffrey Zinden. They were students in William and Mary's Masters in Public Policy program and my research assistants during their time here. The fruits of their labor can be found in the gray boxes containing the snippets that complement the formal analysis.

A number of William and Mary undergraduates have contributed to the third edition by suggesting improvements to its predecessor. I'm happy to be able to publicly thank Fasil Alemante, Daniel Byler, Bryan Callaway, Jimmy Cao, Sarah Gault, You-Suk Kim, Shane Mangin, Ruoyan Sun, Richard Uhrig, and especially Theresa Long. I'malso grateful to Simon Fung who, as a student at the University of London, drew my attention to an error in the second edition.

I salute my Cambridge University Press editors, Karen Maloney and Stephen Acerra, and editorial assistant Kristina Deusch. Their encouragement and guidance are much appreciated.

This chapter examines decision making by a community (or any group) in a simple model: the community must choose from a finite set of mutually exclusive alternatives. (The next chapter endows the model with much more structure by specifying individual utility functions and a production function – and resource constraints. The utility functions will have classical economic properties.)

We look at situations in which a groupmust make a decision that will be binding on all of its members. For example, a class has to determine a time for a review session, a town has to decide whether to build a new school, a nation has to elect a legislature. The resulting choice will have no other implications for personal consumption – in this chapter. Suppose for instance that X, Y, Z, etc. denote alternative ways of spending a fixed amount of government revenue, with the same individual tax burdens in each case. In this setting we can't rule out any ranking of the available options as a possible preference scheme for a member of the group. This makes it very difficult to induce truthful revelation of the hidden characteristic, which in this chapter and the next is the individual's true preference scheme. We want the individuals to reveal enough information about their preferences to enable the system to select the outcome that best reflects those individual preferences.

Clearly, one could write an entire book on the criteria for determining the alternative that “best” reflects individual preferences. Indeed, hundreds of volumes have been written on that theme. In this chapter we set that issue aside and simply determine which selection rules elicit truthful information about individual preferences. Aselection rule is essentially amapping from individual preferences into a social choice, and it must be defined for each possible specification of individual preferences.

VOTING RULES

Although this section examines voting procedures, you are encouraged to think of the candidates standing for election not as individuals seeking careers in government but as alternative packages of public projects. Candidate (or alternative) X may, for example, be a proposal to reduce expenditure on space exploration by a specific amount and to use the proceeds to fund research on the production of energy by nuclear fusion.

This chapter investigates incentives in firms. We explore the hidden action problems of a modern corporation. Section 4.1 compares firms in several leading industrialized countries. Section 4.2 examines the relationship between two senior executives who share the firm's profits and is followed by a brief look at the relationship between the owner and employees in an owner-managed firm (Section 4.3). The rest of the chapter is devoted to the hidden action problem confronting a widely dispersed group of shareholders whose objective is to have the firm that they jointly own maximize the value of their shares. Can they rely on the board of directors to provide the appropriate incentives to the company's management team, even though it is extremely costly for the shareholders to monitor the management and the board members as well?

A BRIEF TOUR OF SEVERAL COUNTRIES

We are primarily concerned with the attempt of a firm's owners to obtain a satisfactory return on the capital they supply to the firm. The owners provide financing when they purchase shares in the firm. They also contribute passively every time the firm uses retained earnings to purchase equipment. Firms also borrow financial capital, and in many industrialized countries bank loans are a much more important source of finance than in the United States. All the suppliers of finance want management to function in a way that brings them a high return. However, a chief executive may act in a way that benefits himself or herself at the expense of the suppliers of capital. We refer to this as the agency problem.

One striking difference between the pattern of ownership across countries lies in the role of the financial sector. US banks were prohibited from holding equity in corporations until the repeal of the Glass-Steagall Act in 1999.

This chapter and the next investigate the extent to which an agent can be motivated to act in the principal's interest when the principal cannot determine whether the agent has in fact taken the appropriate action. Agents’ behavior is problematic because their goal is to maximize their own utility. The next chapter is devoted to the specific hidden action problem of motivating workers and management in a firm, with the top executives receiving most of our attention. This chapter examines a wide variety of other issues. In many of these the principal is a surrogate for society as a whole, and the principal's utility is maximized when the agents – the producers and consumers – are all motivated to do their part in contributing to an efficient outcome.

As with all hidden information problems, there are hidden characteristic elements as well as the hidden action element. In fact, some of the topics could have been presented as hidden characteristic problems. For instance, we could study resource allocation from the standpoint of inducing consumers to reveal their hidden preferences and firms to reveal their hidden production technologies so that an efficient outcome can be identified. However, the approach taken in the first section is that of inducing each individual to choose a bundle of goods and services at which his or her marginal rate of substitution equals that of the other consumers. Similarly, when discussing pollution abatement in Section 2, we begin with the fact that the adjustment cost of an individual firm – the firm's characteristic – is hidden from the government. If the firm were simply asked to report its adjustment cost we would have a hidden characteristic problem, belonging in Chapter 5. However, we instead look at an incentive scheme that harnesses the profit motive to induce firms to coordinate their actions so that the adjustment burden falls on the firms that can reduce pollution at the lowest cost to consumers.

Hidden action problems are complicated by the presence of uncertainty. If your car breaks down a week after you bring it home from the repair shop you do not know whether you are the victim of bad luck or shirking by the mechanic.