Bidding in a Possibly Common-Value Auction

We analyze a second-price auction with two bidders in which only one of the bidders is informed as to whether the object is valued commonly. We show that any equilibrium strategy of the bidder who is uninformed must be part of an equilibrium when both bidders instead know that the auction is not common value, regardless of the way in which the values are different. We derive su¢ cient conditions for equilibrium existence

Misselling through Agents * Roman Inderst †

Abstract This paper analyzes the implications of the inherent conflict between two tasks performed by direct marketing agents: prospecting for customers and advising on the product's "suitability" for the specific needs of customers. When structuring salesforce compensation, firms trade off the expected losses from "misselling" unsuitable products with the agency costs of providing marketing incentives. We characterize how the equilibrium amount of misselling (and thus the scope of policy intervention) depends on features of the agency problem including: the internal organization of a firm's sales process, the transparency of its commission structure, and the steepness of its agents' sales incentives. When purchasing unfamiliar products, consumers often rely on information and advice provided by representatives of the seller. This creates the possibility of "misselling," the questionable practice of a salesperson selling a product that may not match a customer's specific needs. 1 This problem is particularly severe in markets for technically complex products, such as consumer electronics, auto repairs, medical services, and retail financial products including securities, pensions, insurance policies, and mortgages. An important feature of these markets is that the seller often deals with the customer through an agent, rather than directly. For example, financial brokers typically recommend purchase of a specific product after inquiring about their customers' particular circumstances and needs. The possibility of abuse has led to regulation in some of these markets, most notably for securities transactions. The Financial Industry Regulatory Authority (FINRA, the major self-regulatory organization for securities firms operating in the United States) mandates that brokersdealers make a reasonable effort to obtain information about the individual characteristics of their (non-institutional) customers and to ensure that their recommendations are "suitable" to customers' financial situations and needs. 2 Firms that make unsuitable recommendations are sanctioned through FINRA disciplinary procedures. ' Standard Chartered Bank, 2005) reports the following apt illustration: "Typically, mis-selling is associated with investment products when there may have been a failure to disclose all the associated risks or where an investment product is inappropriate to a customer's needs. For example, a product with a long tenor [sic] (eg ten years) may have a guaranteed repayment of principal only on maturity date, but if prematurely liquidated it may not repay the full principal. This may result in mis selling if it is sold to customer who may have had a short term need for cash or to a customer who is 70 years old." 2 FINRA was formed in 2007 through a consolidation of the enforcement arm of the New York Stock Exchange, NYSE Regulation, Inc., and the National Association of Security Dealers (NASD). NASD Conduct Rule 2310(a) 'Recommendation to Customers (Suitability),' originally adopted in 1939, prescribes: "In recommending to a customer the purchase, sale or exchange of any security, a member shall have reasonable grounds for believing that the recommendation is suitable for such customer upon the basis of the facts, if any, disclosed by such customer as to his other security holdings and as to his financial situation and needs." Added in 1991, Rule 2310(b) 'Broker's Duty of Inquiry' further requires: "Prior to the execution of a transaction recommended to a non-institutional customer, other than transactions with customers where investments are limited to money market mutual funds, a member shall make reasonable efforts to obtain information concerning: (1) the customer's financial status; (2) the customer's tax status; (3) the customer's investment objectives; and (4) such other information used or considered to be reasonable by such member or registered representative in making recommendations to the customer." In addition, Rule 3010 imposes a duty of supervision on the firm employing the broker-dealer. 3 According to Lewis Lowenfels and Alan R. Bromberg (1999), "unsuitability claims are the most common and yet the most ambiguous of all customer claims." Regulatory bodies may, in addition, support customers who claim compensation. Such compensation can be substantial, as witnessed by recent highprofile misselling scandals following the liberalization of the U.K. financial industry in the 1980s. After a full review of private pension sales in 1994, financial institutions reportedly paid out a total compensation 1 This paper analyzes the possibility of misselling through the lens of the agency relationship between the selling firm and its salesforce. We argue that the risk of misselling is particularly acute when the firm hires the same agents to both prospect for new customers and provide product advice. When the firm provides steeper incentives-for example, because the presence of more firms makes it harder for agents to locate new customers-then agents will be more tempted to inflate the perceived value of the product, or to recommend purchase even if the product is inappropriate for the customers they identify. At the heart of our model lies a multi-task problem that is inherent to the practice of direct marketing. An agent who markets a product directly to customers must first prospect for potential customers and interest them in the product, and second advise customers on the suitability of the product (including the provision of accurate information). The incentives necessary to induce search effort subsequently tempt the agent to advise purchase indiscriminately. Firms that missell through their own employees may be held vicariously liable or may damage their reputation with customers. Similarly, when misselling takes place through independent intermediaries, firms risk being sued or facing regulatory sanctions (including loss of license). Therefore, firms should have a vital interest in ensuring that their agents comply with the chosen standard of advice. However, ensuring compliance is costly for the firm, as it may require internal reviews or result in rents for the agents. 4 Through the use of contingent commissions, which are clawed back in cases of alleged misselling or when dissatisfied customers cancel a contract, the resulting agency cost to the firm can be reduced. 5 We show that an agent's expected cost of prospecting for customers, the internal organization of a firm's sales process, and the transparency of the commission structure all affect the firm's own tolerance towards misselling. Importantly, it is only through the agency of £12 billion. Compensation is still being paid for the misselling of endowment mortgages, which bundle mortgages with risky investments. See also footnote 22. 4 Sellers can use a number of internal controls to monitor agents and to limit their discretion when making recommendations to customers. For example, sellers use internal compliance officers and Customer Relationship Management (CRM) systems to regularly audit their agents' "fact finds." The audit trail for the transaction allows the seller to monitor the agent's performance more easily and to resolve disputes over allegations of misselling. 5 In an extension of the baseline model, we show that agency costs may be limited further if advisers are relieved (to some extent) of the task of prospecting for customers (for example, when bank managers are only advising incoming clients in a bank's local branch, while client traffic is driven by the bank's marketing campaign). 2 relationship that these factors affect the potential for misselling. Casting the firm as an entrepreneurial entity instead-akin to a self-employed lawyer or doctor, as in the extant literature on credence goods-overlooks the role played by these factors. As we argue, this could be particularly problematic in evaluating the scope of possible policy intervention, say through imposing regulations or probing into cases of alleged misselling. In addition, while the presence of the internal agency problem strengthens the case for intervention, it also calls for policymakers and regulators to adopt a more fine-tuned approach-for example, by adapting their response to the organization of the sales process and the prevailing intensity of competition. In our model, the price of the product is determined endogenously. On the one hand, the suitability standard that customers expect to prevail affects the maximum price they are willing to pay. On the other hand, the price also affects the firm's incentives to expand sales by tolerating a lower suitability standard. Even though customers do not observe the agent's incentives in our baseline scenario, they have correct expectations in equilibrium about the commission structure and the resulting suitability standard. Given that the expectation of misselling reduces customers' willingness to pay, the firm would benefit ex ante from committing to pay ex post penalties for misselling. Firms might be able to achieve some commitment through self-regulatory organizations, such as FINRA. 6 However, we show that even when firms have the same commitment power as a policymaker, the suitability standard set under self-regulation is still too low from a welfare perspective. In addition to imposing penalties for misselling, regulators could mandate disclosure of the commissions paid to agents, as is becoming increasingly common in some countries and markets. 7 We show that the disclosure of commissions partly deters firms from lowering their standards. When observing that the firm offers less steep incentives to the agent, customers are reassured that the suitability standard has increased; hence, they are willing to pay more, to the benefit of the firm. As more financial decisions end up in the hands of consumers, for example with the shift from defined benefit pension plans to 401(k) plans in the United States, regula-6 While SEC regulation requires that all brokers-dealers belong to a self-regulatory organization, in other markets membership in such organizations is voluntary. For example, insurance brokers can apply for membership in the Insurance Marketplace Standards Association (IMSA), a voluntary self-regulatory organization active in setting and enforcing ethical standards for the sale of individual life insurance, long-term care insurance, and annuities. 7 See Section 6. 3 tors are grappling with the interaction between product providers, advising agents, and consumers-Howell E. Jackson's (2007) "trilateral dilemma." 8 As is common for the retailing of financial services, the U.S. mortgage industry also relies heavily on third-party agents. 9 In the context of our model, we analyze how agents' compensation and suitability standards change as firms resell contracts (such as loans)-a practice that is currently attracting regulators' attention. It remains to be seen how courts and policymakers will deal with the fallout from the recent turmoil in the subprime mortgage market. Beyond financial and insurance services, our model applies more broadly to situations in which marketing agents are tempted to inflate the perceived value of products. 10 For instance, a salesperson may praise certain features but hide others when trying to convince a client to switch to a particular calling plan, or utility contract, either of which may be sufficiently complex to make such deception successful. 11 The rest of the paper is organized as follows. Section 1 reviews the related literature. Section 2 formulates the baseline model. Section 3 characterizes how the firm should optimally compensate the agent. Section 4 analyzes the equilibrium that results when the customer does not observe the agent's compensation. Section 5 discusses the effect of agency on the equilibrium outcome and on the scope for policy intervention. Section 6 turns to the equilibrium when the agent's compensation scheme is transparent. Sections 7 to 9 extend the model to investigate the role of the internal organization of the sales process, the possibility of contract resale, and the effect of changes in the amount of competition for customers. Section 10 concludes. Appendix A presents a toy model of the 8 Legal scholars are paying increasing attention to the role of contingent commissions and premiums in the form of yield spread premiums to mortgage brokers, brokerage commissions in investment management, contingent insurance commissions, or fees and kickbacks in real estate settlement transactions. These commissions are feared to tempt advisors to "steer" clients to unsuitable products. See, for instance, Jackson and Laurie Burlingame (2007) and, with a particular focus on contingent commissions, Daniel Literature This paper contributes to the analysis of optimal compensation for a direct marketing agent who must be incentivized simultaneously to sell and not to missell. When analyzing the optimal compensation structure (salary and commission) for sales agents, the marketing literature has traditionally focused on the classic trade-off between risk-sharing and incentives (see Amiya K. Basu, Rajiv Lal, V. Our model hinges on the conflict between a sales agent's incentives to prospect for customers and to provide adequate advice. The compensation needed to elicit effort on one task (prospecting for customers) creates a conflict of interest between the firm and the agent on the second task (providing adequate advice). This conflict generates a multi-task agency problem Consideration of the firm's agency problem is novel to the literature on credence and experience goods, following Michael R. 14 In their analysis Hagerty By focusing on this agency problem, we highlight the two-way interaction between the internal organization of the sales process and the regulatory framework. 15 Model Consider a risk-neutral firm selling a single product through a risk-neutral agent who is asked to both prospect for customers and advise them. The agent is protected by limited liability, and hence can only receive positive compensation from the firm. By exerting sales effort at private disutility c S > 0, the agent contacts a potential customer with probability μ > 0. 16 16 Think of the agent as either contacting previous clients or prospecting for new customers. The cost c S may be required to make customers aware of the existence of the (possibly new) product. 6 In addition, the agent assists customers in deciding whether the product (or service) is suitable for their specific needs. To capture the uncertainty about the match between customer preferences and product characteristics, we stipulate that there are two customer types, θ = l, h. A customer of type θ derives utility u θ from acquiring the product, with u l < 0 < u h . 17 We allow for the firm's cost of serving the customer, k θ > 0, to be type dependent. 18 Given this specification, a sale made to a type-l customer results in both net loss for the customer and inefficiency from a welfare perspective. The prior probability that θ = h is given by 0 < q < 1, which is also the only information the customer has about the type. The agent privately observes a noisy presale signal s ∈ [0, 1] about the customer's type. 19 Without further loss of generality, we stipulate that s is realized according to the type-dependent distribution functions F θ , where F h dominates F l in the Monotone Likelihood Ratio (MLR) order. We assume that the densities f θ (s) are continuous and strictly positive in the interior s ∈ (0, 1), so that the posterior probability q(s) = Pr[θ = h | s] is strictly increasing. Assuming further that f h (1) > 0, f l (0) > 0, and f h (0) = f l (1) = 0, the signal is fully informative at the boundaries: q(0) = 0 and q(1) = 1. It is convenient to define F (s) as the unconditional distribution of the signal, with density f (s) : When contracting with the agent, the firm cannot condition directly on the agent's effort or the customer's type, because the firm does not observe them. Instead, the firm can condition the agent's compensation first on whether a sale has been made, and second on a post-sale signal about the customer's type. We specify that the post-sale signal reveals with probability 0 < ψ < 1 whether a sale was made to a type-l customer. For instance, the signal could originate from the complaints of disgruntled customers. In this case, ψ corresponds to the conditional probability with which a sale to a type-l customer results 17 Utilities are taken to be net of the respective next-best option. For instance, retail investment products may have a particular risk-return profile that is not optimal for all investors. Likewise, one product may create a particular tax advantage, though possibly at the cost of higher risk. 18 As discussed in more detail in Section 8, the firm's margin naturally depend on the customer's type for some financial products (such as mortgages or insurance contracts) and long-term service contracts (such as calling plans or utility services-cf. footnote 11). The condition k l > k h may have particular relevance for financial products such as mortgages (see footnote 47). The case with k l < k h may be applicable to insurance products, where type-h customers could represent high-risk customers, who are more likely to receive the contractually stipulated (pooling) indemnity. Finally, the case with k θ = k should apply to most physical goods. 19 Because this is not key to our analysis, we also specify for the moment that this information is available to the agent at no additional cost. See, however, Section 7. 7 in a verifiable complaint. 20 A key parameter in our model is the expected penalty, ρ, that the firm incurs from (mis)selling to a type-l customer. 21 This parameter captures the legal costs and the fines following prosecution for misselling, comprising compensation that must be made to customers. In addition, the firm may suffer a loss in reputation following alleged misselling. In regulated sectors, the firm may face the risk of losing its license, being brought under closer regulatory scrutiny, or being less able to successfully contest future disciplinary actions for alleged misconduct. 22 Note that because the signal s is noisy, even draconian punishment (high ρ) could not ensure that only type-h customers will purchase. Instead, because the firm can be sure to sell only to type-h customers if and only if s = 1, the firm would close down its business if ρ were sufficiently high. 23 We stipulate that a fraction 0 ≤ η ≤ 1 of ρ represents a compensatory transfer to the customer. All of our results hold irrespective of the choice of η. The timing is as follows: 1. The firm sets the product price, p. 2. The firm sets the compensation scheme for the agent. 3. The agent chooses whether to exert effort to prospect for a customer. 4. If the agent exerts effort, then a customer arrives with probability μ. 5. The agent privately observes signal s about the customer's type. 6. The agent advises the customer whether to purchase. 7. The customer decides whether to purchase at price p. 8. Conditional on a sale to a type-l customer, the firm observes a negative signal with probability ψ. 9. Conditional on a sale to a type-l customer, the firm pays an expected penalty ρ, a fraction η of which is rebated to the customer. A key building block of the model is the communication game between the agent and 20 In footnote 29 we argue that our results are robust to alternative specifications of the monitoring technology, provided that the post-sale signal is noisy. 21 The likelihood that disgruntled customers lodge complaints, or that sufficient information of alleged misselling surfaces, may be low. Still, ρ may be substantial if the imposed penalty is sufficiently large. 22 As explained by 8 the customer that takes place at stages 5-7. The agent's preferences depend on the firm's compensation scheme and thus will reflect the preferences of the firm. However, when k l + ρ ≤ k h holds, firm and customer interests are completely misaligned: the firm benefits (weakly) more when selling to type-l customers, while type-h customers benefit strictly more from a purchase. In this case, there is no equilibrium in which the customer follows the agent's advice. We therefore stipulate for now that k l + ρ > k h . 24 We will show that in this case the agent's recommendation results in the customer purchasing the product whenever s ∈ [s * , 1], where we refer to s * as the suitability standard. By choosing the compensation scheme at stage 2, the firm effectively induces the agent to implement a particular suitability standard. Following Grossman and Hart's (1983) twostage approach, Section 3 characterizes the firm's agency costs associated with any given suitability standard. Section 4 then turns to the determination of the optimal standard. 25 Agency Cost of Suitability This section characterizes the compensation scheme that induces a direct marketing agent to implement a given suitability standard s * . We show that to implement a suitability standard s * > 0, the seller must leave a positive rent to the agent-this rent corresponds to the agency costs associated with the standard. Incentive Constraints The agent is protected by limited liability and has an outside option wage of zero. As shown in Proposition 1, it is opti

Private Information of Nonpaternalistic Altruism: Exaggeration and Reciprocation of Generosity

Applying techniques developed by Geanakoplos et al. (1989), this paper analyzes the gift exchange between agents with privately observed nonpaternalistic altruism. I find that gift giving between agents under private information of altruism can be analyzed as a conventional signaling game. After applying standard refinements of signaling games, I show that, over nondegenerate ranges of parameter values, private information introduces systematic biases in agents' behavior. First, agents tend to give larger gifts than under full information. Second, despite that fact that agents have no intrinsic concern for reciprocity or fairness, the more altruistic the recipient is, the more the donor exaggerates the gift size. The second finding gives rise to a new theory of reciprocity according to which private information of unconditional altruism can lead to reciprocal behavior.

Relational contracts, limited liability, and employment dynamics

This paper studies a relational contracting model in which the agent is protected by a limited liability constraint. The agent's effort is his private information and affects output stochastically. We characterize the optimal relational contract and compare the dynamics of the relationship with that under the optimal long-term contract. Under the optimal relational contract, the relationship is less likely to survive, and the surviving relationship is less efficient. In addition, relationships always converge to a steady state under the optimal long-term contract, but they can cycle among different phases under the optimal relational contract