I am a microeconomic theorist, interested in information acquisition, mechanism design and market design.
Stanford University
Graduate School of Business
Assistant professor of Economics
"The optimal learning dynamics is acquiring Poisson signal confirming prior belief."
I study a dynamic model in which a decision-maker (DM) acquires information about the payoffs of different alternatives prior to making a decision. The model’s key feature is the flexibility of information: the DM can choose any dynamic signal process as an information source, subject to a flow cost that depends on the informativeness of the signal. Under the optimal policy, the DM acquires a signal that arrives according to a Poisson process. The optimal Poisson signal confirms the DM’s prior belief and is sufficiently precise to warrant immediate action. Over time, given the absence of the arrival of a Poisson signal, the DM continues seeking an increasingly precise but less frequent Poisson signal.
"An auctioneer with limited commitment and many bidders achieves at most the profit from an efficient auction."
We study the role of limited commitment in a standard auction environment. In each period, the seller can commit to an auction with a reserve price but not future auctions.We characterize the set of equilibrium profits attainable for the seller as the period length vanishes. An immediate sale by efficient auction is optimal when there are at least three buyers. For many natural distributions two buyers is enough. Otherwise, we give conditions under which the maximal profit is attained through continuously declining reserve prices.
"Knowledge about distribution moments leads to the robust optimality of bundling."
We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue robustly against a worst-case distribution of a buyer's valuations within a set of distributions, called an ``ambiguity'' set. We identify the exact forms of robustly optimal selling mechanisms and the worst-case distributions when the ambiguity set satisfies a variety of moment conditions on the values of subsets of goods. We also identify general properties of the ambiguity set that lead to the robust optimality of partial bundling which includes separate sales and pure bundling as special cases.
"Which information cost functions can be rationalized by an underlying process of optimal sequential information gathering? "
This paper develops a theory for the expected cost of optimally acquired information when information can be acquired sequentially. We study the “reduced-form” Indirect Cost functions for information generated by sequential minimization of a “primitive” Direct Cost function. The class of Indirect Costs is characterized by a recursive condition called Sequential Learning-Proofness. This condition is inconsistent with Prior-Invariance: Indirect Costs must depend on the decision-maker’s prior beliefs. We show that Sequential Learning-Proofness provides partial optimality foundations for the Uniformly Posterior Separable (UPS) cost functions used in the rational inattention literature: a cost function is UPS if and only if it is an Indirect Cost that (i) satisfies a mild regularity condition or, equivalently, (ii) is generated (only) by Direct Costs for which the optimal sequential strategy involves observing only Gaussian diffusion signals. We characterize the unique UPS cost function that is generated by a Prior-Invariant Direct Cost; it exists only when there are exactly two states. We also propose two specific UPS cost functions based on additional optimality principles. We introduce and characterize Total Information as the unique Indirect Cost that is Process-Invariant when information can be decomposed both sequentially and “simultaneously”: it is uniquely invariant to the “merging” and “splitting” of experiments. Under regularity conditions, Mutual Information is the unique Indirect Cost that is Compression-Invariant when aspects of the state space can be “freely ignored”: it is uniquely invariant to the to the “merging”and “splitting” of states. We argue that Total Information and Mutual Information represent the normatively ideal costs of, respectively, “producing” and “processing” information.
"Poisson learning creates most dispersed decision time distribution"
An agent acquires information dynamically until her belief about a binary state reaches an upper or lower threshold. She can choose any signal process subject to a constraint on the rate of entropy reduction. Strategies are ordered by ``time risk"---the dispersion of the distribution of threshold-hitting times. We construct a strategy maximizing time risk (Greedy Exploitation) and one minimizing it (Pure Accumulation). Under either strategy, beliefs follow a compensated Poisson process. In the former, beliefs jump to the threshold that is closer in Bregman divergence. In the latter, beliefs jump to the point with the same entropy as the current belief.
"A characterization of payoffs implementable through information design in a bargaining game."
Consider a canonical bargaining problem: a buyer makes a take-it-or-leave-it offer to a seller for a single object. The two parties’ values may be interdependent. We study the set of payoff vectors that can be implemented (in sequential equilibria) using joint information design. We establish, in part constructively, that the set is a triangle characterized by simple feasibility and individual-rationality constraints. We also investigate what is implementable only using information structures in which the seller is more informed than the buyer, or more generally, under a “no signaling” equilibrium restriction. We show that there is then no loss in providing the buyer with no information and only varying the seller’s information; i.e., familiar adverse-selection structures emerge. Our model encompasses monopoly pricing, for which our results augment those of Bergemann, Brooks, and Morris (2015) and Roesler and Szentes (2017).
"In a decentralized market, rating-guided search involves informational externality and endogenously creates statistical discrimination."
We consider a decentralized market where buyers search to trade with sellers of unknown quality. Each buyer targets sellers based on their ratings — a coarse summary (e.g. average) of the seller’s quality collected from previous transactions involving these sellers. We study the implication of a novel informational externality in the rating-guided market: the informational content of the sellers’ ratings is endogenous, depending on the frequency of their trading, but buyers make trading decisions not taking into account their informational effects. First, we show that an improvement in the ratings technology may exacerbate the informational externality, and hence can be welfare-worsening. Second, we extend the baseline model to allow for two ex ante identical demographic groups, and show that the informational externality endogenously generates statistical discrimination. In a stable equilibrium, highly-rated sellers (or workers) in the advantaged group receive more attention than highly-rated sellers (or workers) in the disadvantaged group, leading to discrimination against the latter group in a self-fulfilling fashion. Our analysis implies that an affirmative action policy restores equality, but only in the short run, as the non-discriminative equilibrium is unstable.
"The engagement maximizing content flow keeps the attention-limited user in suspense with Poisson signals."
We consider the problem of a Bayesian agent receiving signals over time and then taking an action. The agent chooses when to stop and take an action based on her current beliefs, and prefers (all else equal) to act sooner rather than later. The signals received by the agent are determined by a principal, whose objective is to maximize engagement (the total attention paid by the agent to the signals). We show that engagement maximization by the principal minimizes the agent's welfare; the agent does no better than if she gathered no information. Relative to a benchmark in which the agent chooses the signals, engagement maximization induces excessive information acquisition and extreme beliefs. An optimal strategy for the principal involves "suspensive signals" that lead the agent's belief to become "less certain than the prior" and "decisive signals" that lead the agent's belief to jump to the stopping region.
"An approximately revenue maximizing multi-item ascending auction."
We design a multi-item ascending auction that is "approximately" optimal, strategically simple, and robust to strategic and distributional uncertainties. Specifically, the auction is rank-guaranteed---ex-post revenue exceeds the maximal sum of the k-highest bidder's values when bidders play non-obviously dominated strategies. Moreover, under distributional uncertainty of valuations, the rank guarantee is asymptotically robustly optimal---it differs from the worst-case total surplus by at most O(1/N).
"A characterization of all joint distributions of time and location implementable via stopping a martingale with bounded variation."
"Venn diagram among (1) sequential learning proofness (2) constant return to scale and (3) prior invariance"
Some useful technical results & preliminary analyses.
"Monopolistic seller of information should design a rich menu to screen buyers holding private information."
I consider the monopolistic pricing of informational good. A buyer's willingness to pay for information is from inferring the unknown payoffs of actions in decision making. A monopolistic seller and the buyer each observes a private signal about the payoffs. The seller's signal is binary and she can commit to sell any statistical experiment of her signal to the buyer. Assuming that buyer's decision problem involves rich actions, I characterize the profit maximizing menu. It contains a continuum of experiments, each containing different amount of information. I also find a complementarity between buyer's private information and information provision: when buyer's private signal is more informative, the optimal menu contains more informative experiments.
Download my Curriculum Vitae here.
Download my Curriculum Vitae here.