arXiv subjects

Weijie Zhong

Publications and source records attributed to Weijie Zhong.

14 recordsLinked to original sources

arXiv2026

Bundling Complements

I study a monopolist selling goods to a buyer with combinatorial preferences. The seller's dual is a minimum-cost flow of the differential virtual value. I characterize two reductions: when the differential virtual value is represented on types, and when this representation is independent of the preference. The distribution then determines the \emph{required directions}, along which the dual transports mass, and the preference the \emph{covered directions} of each bundle; optimality is full coverage. Comparative statics in the preference use this separation: a premium on bundles containing a core of goods models complementarity and widens their covered directions. Two thresholds describe the optimum: above a lower threshold the grand bundle must be offered; above an upper threshold a \emph{core-peripheral} menu --- a bundled core with optional add-ons not sold standalone --- is optimal. The upper threshold is finite if and only if the menu is \emph{inclusive}: it excludes no near-top buyer.

econ.TH↗

arXiv2026

Pricing Access to Dynamic Information Services

A provider sells a \emph{dynamic information service}---a real-time, capacity-constrained process that resolves a customer's uncertainty---to customers who differ privately in urgency. I characterize the revenue-optimal mechanism: deploy a \emph{single}, undistorted information process---the one a customer with unlimited access would most prefer---and screen entirely through a one-dimensional menu of service caps. The provider leaves the product itself undistorted, unlike a Mussa--Rosen monopolist; all screening is absorbed into the cap. The mechanism rationalizes a recurring contractual form---a flat fee for capped access to a common process---spanning AI service tiers, expert-network consultations, and analyst-inquiry retainers. I identify the economic force behind the result, a convexity-preservation property of urgency screening, and give conditions under which the per-unit price declines in the cap.

econ.TH↗

arXiv2026

Exploration and Stopping

We study a decision-maker who explores --- dynamically choosing what to learn --- before stopping to act. We first reduce this dynamic control problem to a static one: any exploration-and-stopping strategy is equivalent to a choice of the joint distribution of the stopped state and the stopping time, subject to one information-budget constraint at each date, and we characterize exactly which distributions are attainable. The reduced problem is a convex program with a linear objective; its dual prices information over time, and the optimal policy concavifies the stopping payoff net of these shadow prices. The curvature of the decision-maker's time preference then governs the shape of optimal exploration: convex time preference induces Poisson exploration, concave time preference confines stopping to a window whose length is controlled by the dispersion of the marginal cost of delay --- forcing an initial phase of pure exploration when the window is short --- and the linear case lies at the boundary between them. We apply the framework to real options, to the speed--accuracy tradeoff in information acquisition, and to a continuous-time exploration contest.

econ.TH↗

arXiv2026

Persuasion and Optimal Stopping

We develop a duality-based first-order approach to dynamic persuasion in optimal stopping problems with general action-, state-, and time-dependent preferences. A direct-communication reduction recasts the design problem as a semi-static program over joint distributions of stopping beliefs and times; strong duality and a near-necessary first-order condition then reduce it to a one-dimensional differential equation in a multiplier that prices the agent's continuation incentive, characterizing the optimum as a \emph{concavification} of a multiplier-augmented payoff. We demonstrate the method in three applications: dynamic binary persuasion, where optimal policies combine \emph{suspense generation} with \emph{action-targeting}; a structural result by which the principal's time-risk preferences alone determine whether suspense is optimal; and dynamic linear persuasion, where the optimum is \emph{dynamic tail-censorship}.

econ.TH↗

arXiv2025

Engagement Maximization

We investigate the management of information provision to maximize user engagement. A principal sequentially reveals signals to an agent who has a limited amount of information processing capacity and can choose to exit at any time. We identify a ``dilution'' strategy -- sending rare but highly informative signals -- that maximizes user engagement. The platform's engagement metric shapes the direction and magnitude of biases in provided information relative to a user-optimal benchmark. Even without intertemporal commitment, the platform replicates full-commitment revenue by inducing the user's belief to remain ``as uncertain as'' the prior until the rare, decisive signal arrives and induces stopping. We apply our results to two contexts: an ad-supported internet media platform and a teacher attempting to engage test-motivated students.

econ.TH↗

arXiv2025

The Cost of Optimally Acquired Information

This paper introduces a framework for modeling the cost of information acquisition based on the principle of cost-minimization. We study the reduced-form \emph{indirect cost} of information generated by the sequential minimization of a primitive \emph{direct cost} function. Indirect cost functions: (i) are characterized by a novel recursive property, \emph{sequential learning-proofness}; (ii) provide an optimization foundation for the popular class of ``uniformly posterior separable'' costs; and (iii) can often be tractably calculated from their underlying direct costs. We apply the framework by identifying fundamental modeling tradeoffs in the rational inattention literature and two new indirect cost functions that balance these tradeoffs.

econ.TH↗

arXiv2025

Lemonade from Lemons: Information Design and Adverse Selection

A seller posts a price for a single object. The seller's and buyer's values may be interdependent. We characterize the set of payoff vectors across all information structures. Simple feasibility and individual-rationality constraints identify the payoff set. The buyer can obtain the entire surplus; often, other mechanisms cannot enlarge the payoff set. We also study payoffs when the buyer is more informed than the seller, and when the buyer is fully informed. All three payoff sets coincide (only) in notable special cases -- in particular, when there is complete breakdown in a ``lemons market'' with an uninformed seller and fully-informed buyer.

econ.TH↗

arXiv2024

Statistical Discrimination in Ratings-Guided Markets

We study statistical discrimination of individuals based on payoff-irrelevant social identities in markets that utilize ratings and recommendations for social learning. Even though rating/recommendation algorithms can be designed to be fair and unbiased, ratings-based social learning can still lead to discriminatory outcomes. Our model demonstrates how users' attention choices can result in asymmetric data sampling across social groups, leading to discriminatory inferences and potential discrimination based on group identities.

cs.GT↗

arXiv2024

Robustly Optimal Mechanisms for Selling Multiple Goods

We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue 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 various moment conditions on the values of subsets of goods. The analysis reveals general properties of the ambiguity set that justifies categorical bundling, which includes separate sales and pure bundling as special cases.

econ.TH↗

arXiv2024

Information Acquisition and Time-Risk Preference

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 unique point with the same entropy as the current belief.

econ.TH↗

arXiv2024

Rank-Guaranteed Auctions

We propose a combinatorial ascending auction that is "approximately" optimal, requiring minimal rationality to achieve this level of optimality, and is robust to strategic and distributional uncertainties. Specifically, the auction is rank-guaranteed, meaning that for any menu M and any valuation profile, the ex-post revenue is guaranteed to be at least as high as the highest revenue achievable from feasible allocations, taking the (|M|+ 1)th-highest valuation for each bundle as the price. Our analysis highlights a crucial aspect of combinatorial auction design, namely, the design of menus. We provide simple and approximately optimal menus in various settings.

econ.TH↗

arXiv2020

The Indirect Cost of Information

We study the indirect cost of information from sequential information cost minimization. A key sub-additivity condition, together with monotonicity equivalently characterizes the class of indirect cost functions generated from any direct information cost. Adding an extra (uniform) posterior separability condition equivalently characterizes the indirect cost generated from any direct cost favoring incremental evidences. We also provide the necessary and sufficient condition when prior independent direct cost generates posterior separable indirect cost.

econ.TH↗

arXiv2018

Selling 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.

econ.TH↗

arXiv2018

Information Design Possibility Set

Let $\mathcal{V}$ be the set of all combinations of expected value of finite objective functions from designing information. I showed that $\mathcal{V}$ is a compact and convex set implemented by signal structures with finite support when unknown states are finite. Moreover, $\mathcal{V}(μ)$ as a correspondence of prior is continuous. This result can be applied to develop a concavification method of Lagrange multipliers that works with general constrained optimization. It also provides tractability to a wide range of information design problems.

math.OC↗