# Tan Gan

# Welcome!

I'm a 4th year Ph.D. student at Yale University.

My research interests are micro economic theory.

My CV.

Contact: tan.gan@yale.edu

# Working Papers

## The Economic of Social Data, joint with Dirk Bergemann and Alessandro Bonatti. Accepted at RAND (arxiv link)

The data externality dramatically reduces consumers' evaluation of their data (either positive or negative), potentially causing distortion in both directions. When the number of consumers is large, the firm can capture the entire value of information by anonymization.

**Abstract:** We propose a model of data intermediation to analyze the incentives for sharing individual data in the presence of informational externalities. A data intermediary acquires signals from individual consumers regarding their preferences. The intermediary resells the information in a product market wherein firms and consumers can tailor their choices to the demand data. The social dimension of the individual data---whereby an individual's data are predictive of the behavior of others---generates a data externality that can reduce the intermediary's cost of acquiring the information. We derive the intermediary's optimal data policy and establish that it preserves the privacy of consumer identities while providing precise information about market demand to the firms. This policy enables the intermediary to capture the total value of the information as the number of consumers becomes large.

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 the optimal non-monetary dominant incentive compatible mechanism with two agents, where the state and the action that each agent cares about are separate and the agent has a single-peak preference over the action. In this framework any dominant incentive compatible decision rule takes the form of contingent delegation: the delegation set provided to one agent depends on the other's report. Focusing on interval delegation, we find a surprisingly general formula for the optimal mechanism. The input of the formula is the solution of two simple single-agent delegation problems, in which the other agent is assumed to receive no constraint at all and report truthfully. The special geometric structure of the formula makes the optimal mechanism group strategyproof. It also makes the comparative static analyses very simple. We illustrate the application of the result using examples from previous literature and a new coordination problem.

## Gacha Game: When Prospect Theory Meets Optimal Pricing. (SSRN link)

When consumers are naive, the optimal dynamic pricing is to sell a ``lucky chest'' that delivers the good with some constant probability in each period. The consumer always naively believes she will try her luck just one last time.

Whereas when consumers are sophisticated, it is optimal to include a ``pity system'', where the most unfortunate buyer will ``hit the pity'' in finite time and then purchase the good at full price.

**Abstract:** This paper considers the pricing problem of selling a unit good to a prospect theory buyer. When the realized price is bounded from below, the optimal price exists and has at most three support: the negative price right at the lower bound, the zero price, and a positive price. This result of optimal pricing under complete information can be used to solve the static mechanism design when the consumer's value is private. The static mechanism is without loss if the buyer knows her dynamic inconsistent preference caused by probability weighting. If the consumer is naive, however, the seller can potentially gain more profit from a dynamic pricing process. I solve the generically unique optimal dynamic selling strategy under complete information, where it is optimal to sell a ``lucky chest'' that delivers the good with some constant probability in each period. Until she finally gets the good, the consumer always naively believes she will try her luck just one last time.

## Optimal Contracts for Data Generators. (SSRN link)

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.