The theme of this chapter is informational asymmetry, which is not the same as the differences of beliefs considered at various points in earlier chapters. Beliefs may differ without there being a consensus that any single person's opinions are intrinsically superior to anyone else's. In some situations, however, it will be clear to all parties involved that some of them are better informed than others. When a principal employs an agent to carry out actions whose outcomes are uncertain – for example, when an absentee landlord engages a farm manager – the latter will evidently be in a better position to know about any shirking or opportunistic behavior he chooses to engage in. As another example, an expert jeweler will evidently be more familiar with the quality of the diamonds he offers for sale than will an ordinary prospective purchaser. We will be considering the first type of situation in Section 8.1 under the heading of hidden actions or moral hazard. Sections 8.2 and 8.3 explore aspects of the second type of situation, the problem of hidden knowledge or adverse selection. In each case the challenge facing the lesser-informed party is to design an incentive scheme (a contract) aimed at mitigating the effects of informational asymmetry.

The primary focus in this chapter will be on the choices made (the contracts designed) by a less well-informed decision maker or principal who has monopoly power. In the case of hidden actions, introducing competition among principals affects the analysis in only a minor way (see Exercise 8.1.2). On the other hand, in the case of hidden knowledge, when a number of less-informed transactors compete with one another, subtle issues arise regarding the nature of equilibrium. For this reason we defer a discussion of competition and hidden knowledge until Chapter 9.

In Part I, dealing with the economics of uncertainty, after covering the “terminal” decisions of the individual in Chapters 1 through 3 we moved on in Chapter 4 to consider market equilibrium. And similarly here in the realm of the economics of information: having examined individuals’ “nonterminal” (informational) decisions in Chapter 5, we now turn to the analysis of the market equilibrium generated thereby.

A first key distinction is between public and private information. If an information service provides public information, decision makers throughout the economy will be attempting to revise their portfolios in the light of their changed beliefs. Consequently, asset prices will adjust. In particular, market values will rise for those assets paying off more handsomely in states of the world now regarded as more likely. If, on the other hand, the message provided is strictly private, an informed party may be able to profit in various ways without any noticeable effect upon prices. However, as we shall see, almost always there are processes at work tending to “publicize” private information. Sometimes this occurs because the informed individual can gain by intended disclosure of his data, for example, if he sells it to others. Or sometimes there may be unintended leakage into the public domain – owing, perhaps, to the fact that the uninformed can monitor the behavior of those who are informed. These more difficult problems are reserved for later in this chapter; only fully public information will be examined initially.

In this chapter, we address a basic problem in decision making under uncertainty: how should an individual select consumption across different states of nature so as to maximize his expected utility? The trick is to view consumption in one state of nature as a separate good from consumption in another state of nature. We then apply an indispensable technique in microeconomics – indifference curve analysis – to the problem to obtain the Fundamental Theorem of Risk Bearing. This theorem is directly applicable only when all state claims are available, i.e., for each state there is a good that pays if and only if that state obtains. However, trading in state claims is usually not a feasible option. Therefore, we generalize to a model with assets, where each asset is viewed as a vector of payoffs, one for each state of nature. This leads to the Risk-Bearing Theorem for Assets Markets. Next, we investigate risky choices made by an individual who cares only about the mean and standard deviation of his consumption. We end the chapter with a model of state-dependent utility.

The individual's best action under uncertainty – the “risk-bearing optimum” – involves choosing among prospects x ≡ (c; π) ≡ (c1, …, cS; π1, …, πS) where the cs are the state-distributed consequences and πs are the state probabilities. In the realm of the economics of uncertainty proper, before turning to the economics of information, the individual's probability beliefs π remain constant and so c1,…, cS are the only decision variables. In general, each cS represents the multi-good basket that the individual is entitled to consume if state s occurs. For simplicity, however, we will often think in terms of a single generalized consumption good (“corn”). Then cs would simply be the individual's state-s entitlement to corn if state s occurs, and the risk-bearing problem is how to choose among alternative vectors (c1,…, cs) of “corn incomes” distributed over states of the world. Unless otherwise indicated, when the symbol cs is described as representing “income” the implication is that we are using the simplified model of a single consumption good.

All human endeavors are constrained by our limited and uncertain knowledge – about external events past, present, and future; about the laws of nature, God, and man; about our own productive and exchange opportunities; about how other people and even we ourselves are likely to behave. Economists have, of course, always recognized the all-pervasive influence of inadequate information, and its correlate of risk, on human affairs. But only in the period after the Second World War did an accepted theory of uncertainty and information begin to evolve. This theory provides a rigorous foundation for the analysis of individual decision making and of market equilibrium, under conditions where economic agents are unsure about their own situations and/or about the opportunities offered them by market dealings.

With recent explosive progress in the analysis of uncertainty, the topic can no longer be described as neglected. Nor have the advances been “merely academic.” The economic theory of uncertainty and information now flourishes not only in departments of economics but also in professional schools and programs oriented toward business, government and administration, and public policy. In the world of commerce, stock market analysts now regularly report measures of share-price uncertainty devised by economic theorists. Even in government and the law, formal analysis of uncertainty plays a role in dealing with issues like safety and health, allowable return on investment, and income distribution.

We revisit a theme of the last few chapters – the interplay of private information and strategic behavior. Some of the questions addressed here were examined earlier, in Chapters 5 and 6, but not in a setting with explicit strategic behavior. In Section 12.1, the incentive of an expert to transmit his information to an uninformed decision maker is investigated. The expert controls the amount of information revealed in order to influence the action of the uninformed individual. We studied the problem of inducing an expert to reveal information truthfully in Section 5.3.1. What is different here is that the payment to the expert cannot depend on the reported information. The question of costly acquisition of information is re-examined in Section 12.2. As in Section 6.3, inefficient acquisition of information can be traced back to a divergence between the private and social value of information.

In the rest of the chapter, we ask how well private information dispersed among individuals can be aggregated when individuals communicate only through their actions. In Section 12.3 we investigate information aggregation when individuals take actions – whether or not to adopt a certain behavior – in sequence. Private information is conveyed only through actions. Individuals care only about the information content of actions of their predecessors. In this setting there is a tendency to herd on similar actions, which blocks information transmission and makes information aggregation very inefficient.

In Part I of this book, covering the economics of uncertainty, the key topics addressed were (1) individuals’ optimizing “terminal” choices with regard to the bearing of risk, and (2) the market equilibrium determined by the aggregate of such individual decisions. In turning here in Part II to the economics of information, we will similarly be considering issues on individual and on group decision making. On the individual level, the central question is: supposing you could get additional information before having to make a terminal decision, how ought you to decide whether and how much information to collect? On the group level, the main question is: what is the nature of the overall equilibrium that arises when some or all individuals undertake such “informational” actions?

After some introductory discussions, the present chapter first analyzes individuals’ decisions as to the acquisition of information. We then consider the informational choices of groups, since the necessity to act as a collectivity has significant consequences for the nature and amount of information desired. Later chapters take up the implications for market equilibrium.

We introduce a model for decision making under uncertainty that will be our workhorse throughout the book. Uncertainty is modeled with a set of states of nature, one of which will occur. The decision maker or individual has a probability distribution over the states of nature that represents his (or her) subjective beliefs about the likelihood of different states of nature. This individual chooses actions and actions have consequences. The consequence for the individual depends on the state of nature and his choice of action. The states of nature are represented in a way that the probabilities of states are unaffected by the individual's actions. The individual's preferences over consequences are captured by a utility function. The probability distribution over states of nature and the utility function over consequences, both of which are subjective, are combined by the expected-utility rule to induce an expected utility over actions.

An individual must choose among acts – or synonymously, he or she must make decisions, or select among actions, options, or moves. And, where there is uncertainty, nature may be said to “choose” the state of the world (or state, for short). You decide whether or not to carry an umbrella; nature “decides” on rain or sunshine. Table 1.1 pictures an especially simple 2 × 2 situation. Your alternative acts x = (1, 2) are shown along the left margin, and nature's alternative states s = (1, 2) across the top. The body of the table shows the consequences cxs resulting from your choice of act x and nature's choice of state s.

The last few chapters investigated strategic interaction between players in a variety of settings. However, the analysis presumed a one-time interaction among players. This chapter inquires into the further strategic opportunities that are introduced when individuals interact with one another repeatedly.

Long-run relationships lead to two types of phenomenon. First, the set of utility payoffs that can be supported as equilibrium outcomes expands. This may be achieved by threatening to punish opponents in later periods of play if they deviate from a sequence of actions that yields the desired utility payoffs. Second, an individual with private information should be able to make favorable information about himself (information that he is a high-quality or otherwise desirable trading partner) credible by actions taken in the early periods of a long-run relationship. That is, an individual should be able to develop a reputation.

The Multi-Period Prisoners’ Dilemma

Let us begin by examining the Prisoners’ Dilemma. In Table 11.1, each individual i(i = 1, 2) may choose to play either “Defect” (strategy x1) or “Cooperate” (strategy x2). The Prisoners’ Dilemma environment is defined by the ranked payoffs in Table 11.1 if e > f > g > h. Table 11.2 is a numerical example.

In the previous chapter we modeled situations with a large number of informed individuals on one side of the market, for example, potential purchasers of insurance who are aware of their individual likelihoods of suffering loss, or potential buyers who are aware of their own reservation prices. On the other side of the market we assumed a relatively uninformed individual possessing some degree of monopoly power – the insurance company, or the monopoly seller. The main issue addressed was contract design: an insurance deductible option to separate the better from poorer risks, or a schedule of options whereby the monopolist might induce the different types of buyers on the other side of the market to reveal themselves.

This chapter relaxes the assumption that the uninformed transactor has no close competitors. Instead, in each market a number of decision makers compete with one another in the design of contracts intended to separate the different types of trading partners they might be dealing with.

In Section 9.1 we consider situations where the traders on the uninformed side of the market move first, offering contracts aimed at screening their possible trading partners. Later, Section 9.3 takes up the opposite case in which the parties on the informed side of the market take the initiative, signaling their respective types by some choice of action. Interpolated between these two analyses is a discussion in Section 9.2 of “reactive equilibrium” in information-revealing situations.

Market institutions come into place to solve extant problems. For example, with the advent of large corporations and multi-location merchandising in the early nineteenth century, posted prices replaced bargaining as the preferred method of retail. More recently, prompted by advances in technology, which make it possible to serve geographically-dispersed bidders, auctions have increased in popularity. At the same time, in transactions involving real estate or cars, prices are determined through negotiations. In this chapter we explore some of the reasons underlying this variety of selling methods. In Sections 10.1 and 10.2 we assume that the seller has the ability to choose and commit to any selling method she likes. Under this assumption, the seller will find it optimal to either post a take-it-or-leave-it price or conduct an auction. When this assumption is relaxed (in Section 10.3), it leads to bargaining between the seller and the buyer.

Posted-Price Markets

A seller has one indivisible object to sell to a buyer. The seller's cost is normalized to zero. The buyer values the object at V ⩾ 0. The seller does not know V and believes that it is drawn from a probability distribution F(V) with positive density f(V). The seller has the power to decide how to sell the object and can choose any market institution that she likes. What should the seller do?

The elements of the decision problem under uncertainty – the individual's preferences, opportunities, and beliefs – were surveyed in Chapter 1. We distinguished between terminal choices, actions undertaken on the basis of given probability beliefs (covered in Part I of this volume), and informational choices, actions designed to improve one's knowledge of the world before a terminal decision has to be made (to be covered in Part II). Chapter 2 analyzed the individual's risk-bearing optimum, the best terminal action to take in the face of uncertainty.

We now want to explore how these optimizing decisions change in response to variations in the person's character or situation (his or her wealth, tastes for risk, the endowment of goods, the market prices faced, and so forth). Modeling the before-and-after effects of such “parametric” changes, without attending to the dynamics of the actual transition path from one solution to another, is called the method of comparative statics. This chapter is devoted to the comparative statics of the individual's risk-bearing optimum.

Measures of Risk Aversion

The individual’s risk-bearing optimum depends critically upon his attitudes toward risk. And, since parametric changes generally involve positive or negative wealth effects, it will often be crucial to take into account how attitudes toward risk vary as a function of wealth.

For the most part, the analysis to this point has dealt with event uncertainty. Individuals were mainly uncertain about nature's choice of state of the world. In the following chapters the focus shifts to strategic uncertainty, where the best course of action for individual A depends upon individual B's choice, and vice versa. So the main risks that a person has to deal with concern the actions and reactions of others. A first step is the choice of an equilibrium concept for such an environment, which turns out to be a subtle and still controversial issue. As usual, our discussion will not attempt to address formal issues of existence or uniqueness of equilibrium. Our aim instead is to provide an intuitive interpretation of the key ideas.

Dominant Strategy

We begin with the Prisoners’ Dilemma, a game that is easy to analyze. The story behind this game is as follows. Two accomplices have been arrested on suspicion of committing a major crime. The prosecutor does not have sufficient evidence to convict them of this crime. Without a confession from at least one of the two accomplices the prosecutor can only send them to prison for one year for the lesser charge of illegal possession of weapons. The two accomplices (or prisoners) are locked up in different cells and cannot communicate with each other. The prosecutor approaches each of them separately and says, “If you confess and your friend does not then I will drop all charges against you. On the other hand, if your friend confesses and you do not then you will do 10 years. If you both confess then I’ll see to it that you get parole after 5 years in prison. Think hard about what you want to do and let me know tomorrow morning.”