# Tan Gan

# Welcome!

I'm a job market candidate at Yale University.

My research interests are microeconomic theory.

Education

PhD in Economics, Yale University 2018-2024 (Expected)

BSc in Mathematics, Peking University 2014-2018

Email: tan.gan@yale.edu

# Publications

## The Economics of Social Data joint with Dirk Bergemann and Alessandro Bonatti Published at Rand Journal of Economics (2022)

The data externality (either positive or negative) makes consumers dramatically under-evaluate the consequence of sharing their data. While exploiting the data externality, the intermediary optimally preserves the privacy of identities if and only if doing so increases social surplus.

Abstract: A data intermediary acquires signals from individual consumers regarding their preferences. The intermediary resells the information in a product market wherein firms and consumers tailor their choices to the demand data. The social dimension of the individual data---whereby a consumer's data are predictive of others' behavior---generates a data externality that can reduce the intermediary's cost of acquiring the information. The intermediary optimally preserves the privacy of consumers' identities if and only if doing so increases social surplus. This policy enables the intermediary to capture the total value of the information as the number of consumers becomes large.

## Optimal Contingent Delegation (Undergrad Thesis) joint with Ju Hu and Xi Weng Published at Journal of Economic Theory (2023)

To solve the optimal multi-agent contingent delegation rule, one just needs to solve a much simpler problem: the optimal single-agent delegation rule where the other agent is assumed to receive no constraint and report truthfully.

Abstract: This paper investigates a two-agent mechanism design problem without transfers, where the principal must decide one action for each agent. In our framework, agents only care about their own adaptation, and any deterministic dominant incentive compatible decision rule is equivalent to contingent delegation: the delegation set offered to one agent depends on the other's report. By contrast, the principal cares about both adaptation and coordination. We provide sufficient conditions under which contingent interval delegation is optimal and solve the optimal contingent interval delegation under fairly general conditions. Remarkably, the optimal interval delegation is completely determined by combining and modifying the solutions to a class of simple single-agent problems, where the other agent is assumed to report truthfully and choose his most preferred action.

# Working Papers

Abstract: An informed seller designs a dynamic mechanism to sell an experience good. The seller has partial information about the product match, which affects the buyer's private consumption experience. We characterize equilibrium mechanisms of this dynamic informed principal problem. The belief gap between the informed seller and the uninformed buyer, coupled with the buyer's learning, gives rise to mechanisms that provide the skeptical buyer with limited access to the product and an option to upgrade if the buyer is swayed by a good experience. Depending on the seller's screening technology, this takes the form of free/discounted trials or tiered pricing, which are prevalent in digital markets. In contrast to static environments, having consumer data can reduce sellers' revenue in equilibrium, as they fine-tune the dynamic design with their data forecasting the buyer's learning process.

Prospect Theory, which suggests that consumers have a preference for gambling, provides a rationale for using a stochastic pricing process instead of a static post price to sell unit goods. The optimal mechanism resembles the loot box mechanisms seen in various industries, such as gacha games.

Abstract: I study the optimal pricing process for selling a unit good to a buyer with prospect theory preferences, which provides a theoretical rationale for loot box mechanisms observed in many industries such as gacha games. In the presence of probability weighting, the buyer is dynamically inconsistent and can be either sophisticated or naive about her own inconsistency. If the buyer is naive, the uniquely optimal mechanism is to sell a "loot box'" that delivers the good with some constant probability in each period. In contrast, if the buyer is sophisticated, the uniquely optimal mechanism introduces worst-case insurance: after successive failures in obtaining the good from all previous loot boxes, the buyer can purchase the good at full price.

## Manage Persuasion Robustly: The Optimality of Quota Rules joint with Dirk Bergemann and Yingkai Li (Paper Link)

Quota rules are the optimal robust solution, when the receiver can precommit to a decision rule thereby influencing the strategic presuasion of a sender who has a state-independent utility.

Abstract: We study a sender-receiver model where the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the signal structure and the signal realization that the sender adopts. This framework captures applications where a decision-maker (the receiver) solicits advice from an interested party (sender). In these applications, the receiver faces uncertainty regarding the sender's preferences and the set of feasible signal structures. Consequently, we adopt a unified robust analysis framework that includes max-min utility, min-max regret, and min-max approximation ratio as special cases. We show that it is optimal for the receiver to sacrifice ex-post optimality to perfectly align the sender's incentive. The optimal decision rule is a quota rule, i.e., the decision rule maximizes the receiver's ex-ante payoff subject to the constraint that the marginal distribution over actions adheres to a consistent quota, regardless of the sender's chosen signal structure.

When the principal can jointly design the monitoring and compensation scheme to uniquely implement work under contracting frictions, introducing intra-team competition is beneficial.

Abstract: In a multi-agent setting, we study the optimal design of monitoring and compensation to uniquely implement work under contracting frictions. Our principal monitors workers flexibly but is constrained in the number of messages incorporated into the incentive contract. With only two messages, the optimal contract features two sub-teams competing for a bonus. Infrafirm competition allows workers to have a larger impact on their remuneration, implying lower wages are sufficient to incentivize effort. With more messages, partial misalignment of incentives enables the principal to extract the full surplus from a team whose size grows exponentially in the number of available messages.

# Work In Progress

## Robust Advertisement Pricing joint with Hongcheng Li (Draft, with math details only, available upon request)

If strategic uncertainty is accounted for, the optimal pricing strategy for advertisements features increasing marginal prices for accessing additional consumers. It is also optimal to prioritize attracting sellers of higher quality into the service with higher rent.

Abstract: We consider the robust pricing problem of an advertising platform, which can charge a seller for distributing the hard evidence of the seller's quality to consumers prior to subsequent trading between the seller and consumers. Multiple equilibria arise due to consumer beliefs about the seller's contingent purchases of advertisement. To tackle this strategic uncertainty conservatively, the platform offers menus of disclosure probability and price to maximize its revenue in the least favorable equilibrium. The optimal design consists of a continuum of menus with strictly increasing marginal prices for higher disclosure probabilities. All menus except maximum disclosure are off-path and their existence is to preclude bad equilibrium play. The structure of the optimal solution suggests that volume-based pricing can outperform click-based pricing when strategic uncertainty is taken into account. In addition, the platform prioritizes attracting higher quality sellers to the service. As a result, high quality sellers enjoy higher rents, even though all sellers have the same outside option in the induced equilibrium.

# Notes

Unbiased sub-sample estimation can be used to (robustly) incentivize data generation when the outcome is not contractable.

Abstract: This paper considers the problem of using monetary transfers to incentivize data generation and aims to illustrate the potential of a more dedicated incentive control for data generation in data markets. I consider a linear regression environment, where a principal can collect multiple agents' data to estimate the unknown state, and use data-dependent transfer to incentivize high-quality data generation. The first best outcome can be achieved by a contract that uses subsample estimation to discipline agents' behavior. In addition, the risk that agents bear is diminishingly smaller than the principal as the number of agents grows. I also consider several extensions, including ambiguity averse principal (where GLS estimators are endogenously chosen), general data generation rule, and direct estimation externalities.