We develop models of markets with procrastinating consumers when competition operates — or is supposed to operate — both through the initial selection of providers and through the possibility of switching providers. As in other work, consumers fail to switch to better options after signing up with a firm, so at that stage they exert little downward pressure on the prices they pay. Unlike in other work, however, consumers — falsely expecting to do still better in the future — are not keen on starting with the best available offer, so at this stage they do not generate much price competition either. In fact, a competition paradox results: an increase in the number of firms or the intensity of marketing increases the frequency with which a consumer receives switching offers, so it facilitates procrastination and thereby potentially raises prices. By implication, continuous changes in the environment can, through a self-reinforcing entry or marketing process, lead to discontinuous changes in market outcomes. Sign-up deals serve their classically hypothesized role of returning ex-post profits to consumers extremely poorly, while in other senses they exacerbate the failure of price competition.
Joint with Paul Heidhues and Takeshi Murooka. Updated July 2021.
Steering Fallible ConsumersAbstract:
Online intermediaries with information about a consumer's tendencies often "steer" her toward products she is more likely to purchase. We analyze the welfare implications of this practice for "fallible" consumers, who make statistical and strategic mistakes in evaluating offers. The welfare effects depend on the nature and quality of the intermediary's information and on properties of the consumer's mistakes. In particular, steering based on high-quality information about the consumer's mistakes is typically harmful, sometimes extremely so. We argue that much real-life steering is of this type, raising the scope for a broader regulation of steering practices.
Joint with Paul Heidhues and Mats Köster. Updated August 2022.
Overconfidence and PrejudiceAbstract:
By injecting a single non-classical assumption, overconfidence, into a bare-bones model of how an agent learns from social observations, we explain key stylized facts about social beliefs and factors that influence them, and make additional novel predictions. First, the agent has self-centered views about discrimination: he believes in discrimination against any group he is in more than an outsider does. Second, the agent is subject to in-group bias: the greater is his "index of similarity" with an individual, the more positively he evaluates the individual. Third, these biases are increasing in the agent's overconfidence. Fourth, the biases are sensitive to how he divides society into groups when evaluating outcomes, so changing his way of thinking on this matter can lower his biases. Fifth, however, only specific types of information are helpful in debiasing the agent; e.g., giving him more accurate information about himself increases all his biases, and better information about someone else helps only if it is direct personal information about the individual's quality. Sixth, the agent is prone to "bias substitution," implying that the introduction of a new competitor group leads him to develop a negative opinion of the new group but positive opinions of other groups. Due to its unique blend of predictions, the model is consistent with much evidence invoked for either the statistical or the taste-based theory of discrimination against the other. Methodologically, our analysis is made possible by a novel explicit characterization of long-run beliefs in general high-dimensional misspecified learning models with normal exogenous signals.
Joint with Paul Heidhues and Philipp Strack. Updated June 2020.
Financial Choice and Financial InformationAbstract:
We analyze the implications of increases in the selection of, and information about, derivative financial products in a model in which investors neglect informational differences between themselves and issuers. We assume that investors receive information that is noisy and inferior to issuers' information, and that issuers can select the set of underlying assets when designing a security. In contrast to the received wisdom that diversification is helpful, we show that when custom-designed diversification across a large number of underlying assets is possible, then expected utility approaches negative infinity. Even beyond this limiting case, any expansion in choice induced by either an increase in the maximum number of assets underlying a security, or an increase in the number of assets from which the underlying can be selected, Pareto-lowers welfare. Furthermore, under reasonable conditions an improvement in investor information Pareto-lowers welfare by giving investors the false impression that they can spot good deals. An increase in competition between issuers does not increase welfare, and even increases investors' incentive to acquire welfare-reducing information. Restricting the set of underlying assets the issuer can use -- a kind of standardization -- raises welfare, and once this policy is adopted, increasing investor information becomes beneficial.
Joint with Péter Kondor. Updated May 2017.