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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.

We provide a unified analysis of how dynamic information should be designed in optimal stopping problems: a principal controls the flow of information about a payoff relevant state to persuade an agent to stop at the right time, in the right state, and choose the right action. We further show that for arbitrary preferences, intertemporal commitment is unnecessary: optimal dynamic information designs can always be made dynamically consistent.

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.

We study a Bayesian agent receiving signals over time and then acting. The agent chooses when to stop and act, and prefers to act earlier all else equal. The signals are determined by a principal, who maximizes engagement (the total attention paid by the agent). We show that engagement maximization minimizes the agent's welfare, induces excessive information acquisition (relative to an agent-optimal benchmark), and leads to extreme beliefs. The principal optimally sends only "suspensive signals" that lead the agent to become "less certain than the prior" and "decisive signals" that lead the agent to stop immediately.

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.

We study statistical discrimination of individuals based on payoff-irrelevant social identities in markets where ratings/recommendations facilitate social learning among users. Despite the potential promise and guarantee for the ratings/recommendation algorithms to be fair and free of human bias and prejudice, we identify the possible vulnerability of the ratings-based social learning to discriminatory inferences on social groups. In our model, users' equilibrium attention decisions may lead data to be sampled differentially across different groups so that differential inferences on individuals may emerge based on their group identities. We explore policy implications in terms of regulating trading relationships as well as algorithm design.

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.

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.

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.

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, $\mathcal{V}(\mu)$ 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.