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Description
We characterize the optimal screening mechanism for a monopolist facing consumers with privately known demands, some of whom have limited abilities to misrepresent their preferences. We show that consumers with better abilities to misrepresent information benefit from the presence of consumers who lack such abilities. Whenever the fraction of the latter group is positive, there is no exclusion: the firm supplies a positive quantity of the good to all consumers whose valuations exceed marginal cost of production. Our analysis is motivated by the evidence indicating that some individuals have limited ability to misrepresent themselves and imitate others.
1. Introduction
* The nature and qualitative properties of optimal selling strategies for a profit-maximizing monopolist have been explored by many authors. The relevant literature contains detailed analyses of a broad range of selling mechanisms and marketing and pricing schemes, such as different forms of price discrimination, bundling, and tying (see, e.g., Tirole, 1988), and it encompasses a variety of environments. The most ubiquitous situation is one where the monopolist faces a population of heterogeneous consumers with private information about their preferences. The optimal mechanism in this case can be implemented via a simple nonlinear pricing schedule (e.g., Maskin and Riley, 1984). This is the essence of the Taxation Principle.
In practice, however, firms possessing significant market power do not only employ nonlinear pricing, but also rely on direct communication and interaction with customers. Firms in many industries, such as car dealerships, insurance companies, airlines, and publishers, try to elicit information on income, occupation, demographic status, as well as the tastes and habits of their customers, before making a sale to them.
The evidence shows that firms use such information--which is clearly related to customers' willingness to pay--in order to offer the same goods or services to different customers at different prices. For example, car salespeople employ various methods and techniques to induce customers to reveal their willingness and ability to pay for the car--which is then used to price an automobile. (1) In Internet commerce, it is becoming common for the prices quoted by Internet stores to depend on the path used to access the site. The path itself, i.e., the history of the customer's visits to the store's and other sites and her responses to questions along the way, contains information about the customer's preferences.
Our article is motivated by these two observations: first, that firms often resort to complicated, costly, and sometimes deliberately nontransparent selling procedures (in the sense that customers are often not informed at the outset about all options that are available to them) designed to extract personal information from customers before making a sale to them; second, that firms are able to use this information to price discriminate and sell the same goods at different prices to different customers. These observations are at odds with the standard approach postulating that all consumers are strategic and able to manipulate their private information in any way they like. Indeed, it would be more cost effective for a firm to avoid building a costly selling mechanism and training its staff in interviewing techniques and instead simply offer a nonlinear pricing schedule-which is known to be optimal in the standard environment. Moreover, selling mechanisms that offer identical products or services at different prices depending on the information provided by the customer would not be feasible in a world populated with standard rational and strategic consumers. Such consumers would infer how their responses affect the price and provide answers signalling that their willingness to pay for the good is low.
We reconcile this apparent discrepancy and explain the aforementioned selling practices and mechanisms by considering an environment where not all agents are strategic and rational in the standard sense. In our economy, some agents have limited cognitive ability, knowledge, or ability to misrepresent their true types, any of which prevents them from imitating the behavior of others in a way that would maximize their payoffs.
There are several reasons to believe that such consumers are present in an economy. At the most basic level, some consumers may not understand whether or how their behavior affects their subsequent terms of trade. One may think about such consumers as naive or boundedly rational. (2) For example, car dealers use a complicated technique called "four square negotiating" to elicit information from less witting customers regarding the level of monthly lease payments that they can sustain. (3)
Secondly, an individual may be unable or unwilling to misrepresent her information if she is naturally averse to lying. For some individuals, the act of lying may be associated with stress or discomfort ("blushing," "feeling wrong"), causing a disutility. This may be due to psychological or ethical reasons. (4) Erard and Feinstein (1994, p. 2) argue that "some taxpayers appear to be inherently honest, willing to bear their full tax burden even when faced with financial incentives to underreport their income. Evidence for such inherently honest taxpayers ... is supported by econometric evidence and survey findings" Indeed, experimental evidence confirms that a nonnegligible portion of the population chooses not to lie regarding private information, even though lying increases their monetary payoffs. (5) Alger and Ma (2003) maintain that some physicians have stronger ethics and are not able to exaggerate the medical problems of a patient when requesting coverage from an HMO, while other physicians are willing to do so. Alger and Renault (2006) investigate the notion of conditional honesty: some agents reveal information truthfully provided they perceive the resulting allocation as sufficiently fair. Alger and Renault (2007) suggest a view of honesty as a precommitment, according to which an honest agent reveals her private information if she has committed to truth-telling ex ante. Chen (2000) argues that individuals have a tendency to keep promises, even if it is not always in their self-interest, and shows that this may cause optimal contracts to be incomplete.
Thirdly, some individuals may be unable or find it costly to conceal their personal characteristics when the latter are correlated with observable attributes. For example, an individual's wealth and income level, demographic status, and even preferences can be inferred from observation of that individual's profession, residence, or automobile. Environments where misrepresenting the truth may require costly concealment actions have been studied by Lacker and Weinberg (1989), Maggi and Rodriguez-Clare (1995), and Crocker and Morgan (1998). Lacker and Weinberg (1989, p. 1347) argue that in many instances, "lying about the state of nature requires more than simply sending a false signal regarding one's private information. Often, costly actions must be taken to lend credence to the signals being sent."
Finally, messages may have to be supported by submission of verifiable claims or evidence. For example, telecom firms provide discounts to households that can credibly document their low incomes. Clearly, failure of an individual to produce evidence known to be available to certain types can serve as proof that this individual is of a different type. Then only those with skills and technology to manufacture evidence will be able to mimic others, while those without such technologies will not be able to conceal their private information. (6)
The main goal of our article is to examine how the presence of consumers who have limited ability to misrepresent their private information affects the optimal selling mechanism of a monopolist. In particular, we ask whether and how the monopolist can extract private information from these consumers at little or low cost. The presence of such consumers is incorporated into a standard screening model in the simplest possible way: we assume that a certain fraction of consumers always provides true information about their willingness to pay for the good when asked to report it.
In the context of our model, the reporting of valuations need not be understood literally. It is natural to view it as a reduced form representing the ultimate result of the firm's actions directed at discovering a consumer's willingness to pay (such as interviewing, requesting evidence), as well as the latter's ability or inability to conceal her type. For brevity, consumers who are unable to misrepresent or conceal their private information will be referred to as "honest." However, this term does not pertain exclusively to consumer's ethics. Alternatively, such consumers can be viewed as boundedly rational or naive. All other consumers can misrepresent their valuations costlessly and will do so to increase their payoffs. Such consumers will be referred to as "strategic." Since a strategic consumer can easily imitate an honest one, honesty or bounded rationality, or naivete is not an observable characteristic. So, the firm cannot simply segment the market into two parts, i.e., third-degree price discrimination is not feasible. (7)
We derive the optimal selling mechanism for this environment and characterize its properties. Our analysis consists of two parts. First, we derive an optimal game form. Second, we characterize the unique optimal allocation profile implementable via the optimal game form. In the standard environment where all consumers are strategic, the choice of a game form has no real significance. This is implied by the Revelation Principle (or the Taxation Principle). However, the Revelation Principle does not hold in our setup, because the mechanism designer can typically take advantage of the fact that different consumers have different sets of feasible messages by constructing a game form where some types submit nontruthful reports in equilibrium. We establish that the following game form, which we call a "password" mechanism, is optimal in our case. First, a consumer is asked to report her valuation. Then, depending on her report, she is either offered a specific quantity/transfer pair, or is given a menu of quantity/transfer pairs to choose from. The optimality of the password mechanism stems from the fact that an allocation profile implementable via this mechanism has to satisfy a minimal set of incentive constraints. In particular, no incentive constraints of honest consumers have to be satisfied. Using this mechanism, we characterize the optimal allocation profile for an arbitrary fraction of honest consumers in the population. The presence of honest consumers has the following qualitative effects:
(i) Less distortion for the strategic consumers: the quantities assigned to a subset of strategic consumers--in particular, the ones with low valuations--are strictly higher than in the standard "second-best" case with no honest consumers, but still below the first-best. The quantities assigned to the rest of strategic consumer types (in particular, the ones with high valuations) are the same as in the standard case.
(ii) The quantities assigned to a subset of honest consumer types, including the low-valuation types, are below the first-best level but above the quantities assigned to the strategic types with the same valuations, while the quantities assigned to the rest of the honest consumers, including the high-valuation ones, are at the first-best level.
(iii) No exclusion: all consumers whose valuations exceed the marginal cost of production consume a positive quantity, no matter how small the fraction of honest consumers may be.
(iv) Strategic consumers (as well as the firm) benefit from the presence of the honest ones: the surplus earned by every strategic "consumer" type (and the firm's profits) is higher than in the absence of honest consumers. All honest consumers earn zero surplus.
(v) For larger quantities, an honest consumer is charged strictly more than a strategic one. For low quantities, they pay the same amount.
(vi) Over an initial range of quantities, the firm charges quantity premia.
The last result provides an empirically testable implication of our model, since Maskin and Riley (1984) have found that the optimal tariff exhibits quantity discounts at all quantity levels in an environment with no honest consumers.
The most surprising qualitative property of the optimal allocation profile is the absence of exclusion. Exclusion is a robust feature of the optimal pricing mechanism in a market with no honest types. Except for the nongeneric case of perfectly inelastic demand at price equal to marginal cost (which requires either that there are no consumers with valuations near marginal cost, or that the density of valuations is infinite at this level), a profit-maximizing monopolist will choose not to sell to consumers whose willingness to pay for the good is not sufficiently higher than marginal cost, under both uniform and nonlinear pricing (see Maskin and Riley (1984) or the discussion in the next section for details). Exclusion must also occur in settings with multidimensional private information (see Armstrong, 1996, and Rochet and Chone, 1998).
If the population consisted only of honest types, then absence of exclusion would be natural. So, intuition based on continuity would suggest that the threshold valuation below which consumers are not served continuously decreases to zero as the fraction of honest types increases. The surprising conclusion of our analysis is that this is not so: as soon as the fraction of honest consumers becomes positive, the threshold level immediately goes down to zero.
The prospect of exclusion is troubling, and may be socially unacceptable, especially when it concerns such vital areas as telecommunication, energy, or transportation. It provides a strong argument in support of government regulation of monopolistic industries. Indeed, it is easy to construct simple examples where the monopolist optimally excludes a significant proportion of consumers. (8) In contrast, our no-exclusion result suggests that such concerns may not be well founded. Even unregulated monopolists will optimally serve all consumers whose willingness to pay for the good is above marginal cost, as long as some consumers in the population do not hide their valuations. Further, if the proportion of honest consumers is nonnegligible (as econometric and experimental evidence suggests), then the consumption of most types who would be excluded in a market without honest consumers is substantial (see Table 1 and Figures 1 and 2). (9)
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
The contribution of this article can be summarized as follows. First, we explain why firms often resort to selling mechanisms that attempt to directly elicit information from consumers regarding their willingness to pay, instead of using the much simpler and cheaper method of presenting them with nonlinear tariffs. Second, we contribute to the theory of screening by developing a method that can handle a population including both strategic and nonstrategic agents. We use this method to fully characterize an optimal allocation profile for this complex environment. Technically, our contribution lies in introducing new techniques to solve a particular class of multidimensional screening problems. A more general lesson learned from our results is that predictions derived for environments that include only strategic agents may differ qualitatively from predictions for environments in which some nonstrategic agents are present.
The remainder of the article is organized as follows. Section 2 presents the model. Section 3 introduces the main results, and provides intuition. The proofs are relegated to the Appendix and an online supplement available at www.severinov.com/supplement_screen_nonstrategic.pdf.
2. Model and preliminaries
* A monopoly supplier faces a population of consumers with privately known preferences for the good. Specifically, a consumer with valuation [theta] gets utility u(q, [theta])--t from consuming quantity q of the good, acquired at cost t. The distribution function F([theta]) of valuations in the population is common knowledge. We assume that F(x) is twice continuously differentiable, and the associated density function f(x) is strictly positive with support consisting of a bounded interval. Without loss of generality, we take this interval to be [0, 1]. The consumer's reservation utility level is zero. The firm's cost is additively separable across consumers. (10) We let c(q) denote the cost... |
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