Title: Optimal Queue Design (with Olivier Tercieux)
Abstract: We study the optimal design of a queueing system when agents' arrival and servicing are governed by general Markov processes. The designer of the system chooses entry and exit rules for agents, their service priority---or queueing discipline---as well as their information, while ensuring that agents have incentives to follow the designer's recommendations not only to join the queue but more importantly to stay in the queue. The optimal mechanism has a cutoff structure---agents are induced to enter up to a certain queue length and no agents are to exit the queue once they enter the queue; the agents on the queue receive a service according to a first-come-first-served (FCFS) rule; and they are given no information throughout the process beyond the recommendations they receive from the designer. FCFS is also necessary for optimality in a rich domain. We identify a novel role for queueing disciplines in regulating agents' beliefs, and their dynamic incentives, revealing a hitherto unrecognized virtue of FCFS in this regard.
Abstract: COVID-19 has revealed several limitations of existing mechanisms for rationing scarce medical resources under emergency scenarios. Many argue that they abandon various ethical values such as equity by discriminating against disadvantaged communities. Illustrating that these limitations are aggravated by a restrictive choice of mechanism, we formulate pandemic rationing of medical resources as a new application of market design and propose a reserve system as a resolution. We develop a general theory of reserve design, introduce new concepts such as cutoff equilibria and smart reserves, extend previously-known ones such as sequential reserve matching, and relate these concepts to current debates.
Title: Welfare of Price Discrimination and Market Segmentation in Duopoly
Abstract: We study welfare consequences of third-degree price discrimination and market segmentation in a duopoly market with captive and contested consumers. A market segmentation divides the market into segments that contain different proportions of captive and contested consumers. Firm-optimal segmentation divides the market into two segments and in each segment only one firm has captive consumers. In contrast to the existing literature with exogenous segmentation, price discrimination under firm-optimal segmentation unambiguously reduces consumer surplus for all markets. Consumer-optimal segmentation divides the market into a maximal symmetric segment and the remainder, and yields the lowest producer surplus among all segmentations.
Title: Robust Merging of Information
Abstract: When multiple sources of information are available, any decision must take into account their correlation. If information about this correlation is lacking, an agent may find it desirable to make a decision that is robust to possible correlations. Our main results characterize the strategies that are robust to possible hidden correlations. In particular, with two states and two actions, the robustly optimal strategy pays attention to a single information source, ignoring all others. More generally, the robustly optimal strategy may need to combine multiple information sources, but can be constructed quite simply by using a decomposition of the original problem into separate decision problems, each requiring attention to only one information source. An implication is that an information source generates value to the agent if and only if it is best for at least one of these decomposed problems.
Title: Identifying Present Bias from the Timing of Choices
Abstract: Timing decisions are common: when to file your taxes, finish a referee report, or complete a task at work. We ask whether time preferences can be inferred when only task completion is observed. To answer this question, we analyze the following model: each period a decision maker faces the choice whether to complete the task today or to postpone it to later. Cost and benefits of task completion cannot be directly observed by the analyst, but the analyst knows that net benefits are drawn independently between periods from a time-invariant distribution and that the agent has time-separable utility. Furthermore, we suppose the analyst can observe the agent's exact stopping probability. We establish that for any agent with quasi-hyperbolic β,δ-preferences and given level of partial naivete, the probability of completing the task conditional on not having done it earlier increases towards the deadline. And conversely, for any given preference parameters β,δ and (weakly increasing) profile of task completion probability, there exists a stationary payoff distribution that rationalizes her behavior as long as the agent is either sophisticated or fully naive. An immediate corollary being that, without parametric assumptions, it is impossible to rule out time-consistency even when imposing an a priori assumption on the permissible long-run discount factor. We also provide an exact partial identification result when the analyst can, in addition to the stopping probability, observe the agent's continuation value.
Title: Supply Network Formation and Fragility
Abstract: We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Due to the risk of such supply relationships being idiosyncratically disrupted, firms multisource inputs and strategically invest to make relationships with suppliers stronger. Aggregate production is robust to idiosyncratic disruptions. However, there is a regime in which equilibrium supply networks are fragile, with small aggregate shocks to relationships causing arbitrarily steep drops in output. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.
Title: Communication with Endogenous Deception Costs
Abstract: We study how the suspicion that communicated information might be deceptive affects the nature of what can be communicated in a sender-receiver game. Sender, who observes the state of the world, is said to deceive Receiver if she sends a message that induces beliefs that are different from those that should have been induced in the realized state. Deception is costly to Sender and the cost is endogenous: it increases in the distance between the induced beliefs and the beliefs that should have been induced. A message function that induces the sender to engage in deception is said to be non-credible and cannot be part of equilibrium. We study credible communication in Bayesian persuasion and in cheap-talk games. Importantly, the cost of deception parametrizes the sender’s ability to commit to her strategy. Through varying this cost, our model spans the range from no commitment (cheap-talk), to full commitment (Bayesian persuasion).
Title: A Strong Minimax Theorem for Informationally-Robust Auction Design
Abstract: We study the design of profit-maximizing mechanisms in environments with interdependent values. A single unit of a good is for sale. There is a known joint distribution of the bidders’ ex post values for the good. Two programs are considered:
(i) Maximize over mechanisms the minimum over information structures and equilibria of expected profit;
(ii) Minimize over information structures the maximum over mechanisms and equilibria of expected profit.
These programs are shown to have the same optimal value, which we term the profit guarantee.
In addition, we characterize a family of linear programs that relax (i) and produce, for any finite number of actions, a mechanism with a corresponding lower bound on equilibrium profit. An analogous family of linear programs relax (ii) and produce, for any finite number of signals, an information structure with a corresponding upper bound on equilibrium profit. These lower and upper bounds converge to the profit guarantee as the numbers of actions and signals grow large.
Our model can be extended to allow for demand constraints, multiple goods, and ambiguity about the value distribution. We report numerical simulations of approximate solutions to (i) and (ii).
Title: Optimal Non-linear Pricing with Data-sensitive Consumers
Abstract: We introduce consumers with intrinsic privacy preferences into the monopolistic non-linear pricingmodel. Next to classical consumers, there is a share of data-sensitive consumers who refrain from buyingif their purchase reveals information about their valuation to the monopolist. When the monopolistobserves consumers’ privacy preferences, data-sensitive consumers obtain a pooling schedule, whileclassical consumers obtain the standard non-linear pricing schedule. Data-sensitive consumers witha low valuation obtain a strictly higher utility than classical consumers with the same valuation. Bycontrast, when privacy preferences are consumers’ private information, classical consumers obtain ahigher utility than data-sensitive consumers with the same valuation. Data-sensitive consumers and themonopolist are worse off when privacy preferences are private information, whereas classical consumersare better off. The results are relevant for policy measures that target the data-awareness of consumers,such as the European GDPR.
Title: Robust Monopoly Regulation
Abstract: We study the regulation of a monopolistic firm using a non-Bayesian approach. We derive the policy that minimizes the regulator’s worst-case regret, where regret is the difference between the regulator’s complete-information payoff and his realized payoff. When the regulator’s payoff is consumers’ surplus, he imposes a price cap. When his payoff is the total surplus of both consumers and the firm, he offers a capped piece rate subsidy. For intermediate cases, the regulator uses both a price cap and a capped piece-rate subsidy. The optimal policy balances three goals: giving more surplus to consumers, mitigating underproduction, and mitigating overproduction.
Title: Subjective Causality in Choice
Abstract: An agent makes a stochastic choice from a set of lotteries. She infers the consequences of the lotteries using a subjective causal model represented by a directed acyclic graph. Her choices affect her inferences which in turn affect her choices, so the two together must form a personal equilibrium. We show how an analyst can identify the agent's subjective causal model from her random choice rule. In addition, we provide necessary and sufficient conditions on the rule that allow an analyst to test whether the agent's behavior is compatible with the model.
Title: Assortative Information Disclosure
Abstract: We consider a standard persuasion problem in which the receiver's action and the state of the world are both one-dimensional. Fully characterizing optimal signals when utilities are non-linear is a daunting task. Instead, we develop a general approach to understanding a key qualitative property of optimal signals: their assortative structure, which describes the overall pattern of what states are pooled together. We derive simple conditions-driven by intuitive economic properties, such as supermodularity and submodularity of preferences-for the optimality of positive and negative assortative patterns of information disclosure. Our approach unifies a wide range of previous findings and generates new applications.
Title: Robust Prediction in Games with Uncertain Parameters
Abstract: We consider games with uncertain parameters, where each player may possess any (possibly higher-order) belief about the parameter values. For example, firms may agree on a set of demand functions based on publicly available data, but not a single demand function. As another example, bidders in a first-price auction may imagine that rival bidders are potentially biased due to some behavioral reasons (such as truthful-bidding bias). An analyst who desires to make a theoretical prediction does not know the players' information structure. We define a robust prediction as a set of action profiles such that, given any information structure among the players, there is an equilibrium given that information structure whose equilibrium action profiles are in this set. We show that there is a canonical type space whose equilibrium action profile set is a robust prediction. We argue that the "equilibrium selection" nature of our robust prediction concept may be advantageous in some contexts, such as when the analyst has some idea about "reasonable" equilibria in the game of interest, or when the goal is mechanism design robust to parameter uncertainty.
Title: Virtual Teams in a Gig Economy
Abstract: While the gig economy provides flexible jobs for millions of workers globally, a lack of organization identity and co-worker bonds contributes to their low engagement and high attrition rates. To test the impact of virtual teams on worker productivity, retention and well-being, we conduct a field experiment with 27,790 drivers on a ride-sharing platform. We organize drivers into teams that are randomly assigned to receiving their team ranking, or individual ranking within their team, or individual performance information (control). We find that treated drivers generate significantly higher revenue. Furthermore, drivers in the team ranking treatment continue to be more engaged three months after the end of the experiment. Survey data suggest that peer learning and team identity contribute to the virtual team efficacy.
Title: Weak Monotone Comparative Statics
Abstract: We develop a theory of monotone comparative statics based on weak set order---in short, \textit{weak monotone comparative statics}---and identify the enabling conditions in the context of individual choices, Pareto optimal choices% for a coalition of agents, Nash equilibria of games, and matching theory. Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environments and underlying preferences of agents. We apply the theory to establish existence and monotone comparative statics of Nash equilibria in games with strategic complementarities and of stable many-to-one matchings in two-sided matching problems, allowing for general preferences that accommodate indifferences and incomplete preferences.
Title: Large Auctions
Title: Inaccurate Statistical Discrimination: An Identification Problem
Abstract: Discrimination, defined as differential treatment by group identity, is widely studied in economics. Its source is often categorized as taste-based or statistical (belief-based)—a valuable distinction for policy design and welfare analysis. However, in many situations individuals may have inaccurate beliefs about the relevant characteristics of different groups. This paper demonstrates that this possibility creates an identification problem when isolating the source of discrimination. A review of the empirical discrimination literature in economics reveals that a small minority of papers—fewer than 7%—consider inaccurate beliefs. We show both theoretically and experimentally that, if not accounted for, such inaccurate statistical discrimination will be misclassified as taste-based. We then examine three alternative methodologies for differentiating between different sources of discrimination: varying the amount of information presented to evaluators, eliciting their beliefs, and presenting them with accurate information. Importantly, the latter can be used to differentiate whether inaccurate beliefs are due to a lack of information or motivated factors.
Title: Data and Incentives
Abstract: "Big data" gives markets access to measurements of previously unknown characteristics of individuals. Policymakers must decide whether and how to regulate use of this new data. Besides immediate consequences (such as potential privacy violations), predictions made using this new data may reshape important economic incentives. We propose a model in which a market's forecast about an agent's quality type is based on a traditional performance signal, e.g. worker output, as well as on additional covariates describing those agents. The measurement of new covariates changes agents' incentives to exert effort. We show that the average effect on the effort is completely determined by whether the covariate is informative about the agent's type or about a shock to the performance signal. For a class of covariates satisfying a statistical property we call strong homoskedasticity, this effect is uniform across individuals. More generally, new measurements can have disparate impact, benefiting certain groups of individuals at the cost of others. We apply these findings to characterize when new data improves or reduces social welfare.
Title: Private Private Information
Title: Are Simple Mechanisms Optimal when Agents are Unsophisticated?
Abstract: We study the design of mechanisms involving agents that have limited strategic sophistication. We define a mechanism to be simple if—given the assumed level of strategic sophistication—agents can determine their optimal strategy. We examine whether it is optimal for the mechanism designer who faces strategically unsophisticated agents to offer a simple mechanism. We show that when the designer uses a mechanism that is not simple, while she loses the ability to predict play, she may nevertheless be better off no matter how agents resolve their strategic confusion.
Title: Perceived Competition in Networks
Abstract: We consider an aggregative game of competition in which agents have an imperfect knowledge about the set of agents they are in competition with. We model agent’s perceived competitors by a network in which each agent is assumed to only have information on the activities of their direct neighbors. In this framework, a natural equilibrium concept emerges, the peer-consistent equilibrium (PCE). In a PCE, each agent chooses an action level that maximizes her subjective perceived utility and the action levels of all individuals in the network must be consistent. We decompose the network into communities and completely characterize peer-consistent equilibria by identifying which sets of agents can be active in equilibrium. An agent is active if she either belongs to a strong community or if few agents are aware of her existence. We show that there is a unique stable PCE. We provide a behavioral foundation of eigenvector centrality, since, in any stable PCE, agents’ action levels are proportional to their eigenvector centrality in the network. We illustrate our results with two well-known models: Tullock contest function and Cournot competition.
Title: Robust Mechanism Design and Costly Information Acquisition
Abstract: We examine how a principal can robustly elicit costly information from multiple agents when he cannot verify the state ex post and faces uncertainty about the agents' motives and beliefs. The principal commits to a mechanism that maps agents' messages to outcomes and monetary transfers. The agents decide whether to acquire costly information about the state after which they send messages to the principal. We show that for every social choice function, when the principal knows agents' preferences with probability close to one, there exists a mechanism and a corresponding equilibrium that implements this social choice function with probability close to one regardless of agents' beliefs and higher order beliefs about each other's preferences.
Title: Costly Monitoring in Signaling Games
Abstract: Off-path beliefs are a key free variable in equilibrium analysis of dynamic games of incomplete information. Our starting point is the observation that, if we take into account players’ incentives to monitor past events in the game, then we can sidestep the question of off-path beliefs. We focus on signaling games where the receiver has to pay a cost to monitor the sender’s action. We show that Nash equilibrium is outcome equivalent to any refinement of perfect Bayesian equilibrium that puts restrictions on the receiver’s off-path beliefs. We then characterize all Nash equilibria that can arise across all cost functions. As an application, we consider the case of vanishing costs to provide a micro-foundation for restrictions on off-path beliefs in standard signaling games where the receiver observes for free the sender’s action.
Title: Mandatory Disclosure of Conflicts of Interest: Good News or Bad News?
Title: Minimum Distance Belief Updating with General Information
Abstract: We study belief revision when information is given as a set of relevant probability distributions. This flexible setting encompasses (i) the standard notion of information as an event (a subset of the state space), (ii) qualitative information (\A is more likely than B"), (iii) interval information (\chance of A is between ten and twenty percent"), and more. In this setting, we behaviorally characterize a decision maker (DM) who selects a posterior belief from the provided information set that minimizes the subjective distance between her prior and the information. We call such a DM a Minimum Distance Subjective Expected Utility (MDSEU) maximizer. Next, we characterize the collection of MDSEU distance notions that coincide with Bayesian updating on standard events. We call this class of distances Generalized Bayesian Divergence, as they nest Kullback-Leibler Divergence. MDSEU provides a systematic way to extend Bayesian updating to general information and zero-probability events. Importantly, Bayesian updating is not unique. Thus, two Bayesian DM's with a common prior may disagree after common information, resulting in polarization and speculative trade. We discuss related models of non-Bayesian updating.
Title: When (not) to Publicize Inspection Results
Abstract: Consider the dynamic inspection problems between a principal and several agents. The principal observes the full inspection history, whereas each agent only observes inspections imposed on himself. When inspection resources are limited, the inspection intensity for agents are negatively correlated, and hence each agent cares not only about his own inspection history, but also about the inspection histories of the other agents. The question we address in this paper is, should the principal publicly reveal past inspection history, or should she conceal such information. We show that when the number of agents is low and the inspection resources are scarce, the principal is better off concealing positive inspection history. Similar results hold if instead of limited inspection resources, the inspection cost in each period is convex in the number of inspections.
Title: An Equilibrium Model of Experimentation on Networks
Title: Robust Maximum Likelihood Updating
Abstract: There is a large body of evidence that decision makers frequently depart from Bayesian updating. This paper introduces a model, robust maximum likelihood (RML) updating, where deviations from Bayesian updating are due to multiple priors/ambiguity. The primitive of the analysis is the decision maker's preferences over acts before and after the arrival of new information. The main axioms characterize a representation where the decision maker's probability assessment can be described by a benchmark prior, which is reflected in her ex ante ranking of acts, and a set of plausible priors, which is revealed from her updated preferences. When new information is received, decision makers revise their benchmark prior within the set of plausible priors via the maximum likelihood principle in a way that ensures maximally dynamically consistent behavior, and update the new prior using Bayes' rule. RML updating accommodates most commonly observed biases in probabilistic reasoning.
Title: Agenda-Manipulation in Ranking
Abstract: A committee ranks a set of alternatives by sequentially voting on pairs, in an order chosen by the committee’s chair. Although the chair has no knowledge of voters’ preferences, we show that she can do as well as if she had perfect information. We characterise strategies with this ‘regret-freeness’ property in two ways: (1) they are efficient, and (2) they avoid two intuitive errors. One regret-free strategy is a sorting algorithm called insertion sort. We show that it is characterised by a lexicographic property, and is outcome-equivalent to a recursive variant of the much-studied amendment procedure.