Coarse Information Design (with Wing Suen and Yimeng Zhang), 2025
(NEW version!!!) Revivse and Resubmit at Journal of Political Economy
We study an information design problem with continuous state and discrete signal space. Under convex and S-shaped value functions, the optimal information structure is interval-partitional and exhibits a dual expectations property: each induced signal is the conditional mean (taken under the prior density) of each interval; and each interval cutoff is the barycenter (taken under the value function curvature) of the interval formed by neighboring signals. This property enables an examination into which part of the state space is more finely partitioned. The analysis can be extended to general value functions and adapted to study coarse mechanism design.
(NEW version!!!) Revivse and Resubmit at Journal of Political Economy
We study an information design problem with continuous state and discrete signal space. Under convex and S-shaped value functions, the optimal information structure is interval-partitional and exhibits a dual expectations property: each induced signal is the conditional mean (taken under the prior density) of each interval; and each interval cutoff is the barycenter (taken under the value function curvature) of the interval formed by neighboring signals. This property enables an examination into which part of the state space is more finely partitioned. The analysis can be extended to general value functions and adapted to study coarse mechanism design.
Complete Contracts under Incomplete Information (with Gregorio Curello and Yimeng Zhang), 2024
We study a moral hazard model in which the output is stochastically determined by both the agent's hidden effort and an uncertain state of the world. We investigate how the contractibility of the ex-post realization of states affects the principal's incentive to provide information. While detailed information allows the principal to better tailor the effort levels to the revealed states, coarser information enables the principal to base payments on the ex-post realization of states, thereby designing incentive schemes more effectively. Our main result establishes that when the state is contractible, full information is never optimal; however, when the state is not contractible, full information is optimal under mild conditions.
We study a moral hazard model in which the output is stochastically determined by both the agent's hidden effort and an uncertain state of the world. We investigate how the contractibility of the ex-post realization of states affects the principal's incentive to provide information. While detailed information allows the principal to better tailor the effort levels to the revealed states, coarser information enables the principal to base payments on the ex-post realization of states, thereby designing incentive schemes more effectively. Our main result establishes that when the state is contractible, full information is never optimal; however, when the state is not contractible, full information is optimal under mild conditions.
Optimal Refund Mechanism with Consumer Learning, 2024
Accepted at RAND Journal of Economics
This paper studies the optimal refund mechanism in a setting where an uninformed buyer can privately acquire information about his valuation of a product over time. We consider a class of refund mechanisms that includes both simple return policies, such as no returns or free returns, and stochastic return policies, which allow the buyer to keep the product with some probability upon receiving a (partial) refund. We show that the optimal refund mechanism is deterministic and takes a simple form: either the seller deters buyer learning by offering a low price and disallowing returns, or she implements maximal learning by offering a high price with free returns. The form of the optimal refund mechanism is non-monotone in the buyer's prior belief regarding his valuation, with free returns being optimal only for intermediate priors.
Accepted at RAND Journal of Economics
This paper studies the optimal refund mechanism in a setting where an uninformed buyer can privately acquire information about his valuation of a product over time. We consider a class of refund mechanisms that includes both simple return policies, such as no returns or free returns, and stochastic return policies, which allow the buyer to keep the product with some probability upon receiving a (partial) refund. We show that the optimal refund mechanism is deterministic and takes a simple form: either the seller deters buyer learning by offering a low price and disallowing returns, or she implements maximal learning by offering a high price with free returns. The form of the optimal refund mechanism is non-monotone in the buyer's prior belief regarding his valuation, with free returns being optimal only for intermediate priors.
Information Design in Cheap Talk (with Wing Suen), 2025
An uninformed sender publicly commits to an informative experiment about an uncertain state, privately observes its outcome, and sends a cheap-talk message to a receiver. We provide an algorithm valid for arbitrary state-dependent preferences that will determine the sender's optimal experiment and his equilibrium payoff under binary state space. We give sufficient conditions for informative information transmission. These conditions depend more on marginal incentives---how payoffs vary with the state---than on the alignment of sender's and receiver's rankings over actions within a state. The algorithm can be easily modified to study the canonical cheap talk game with a perfectly informed sender.
An uninformed sender publicly commits to an informative experiment about an uncertain state, privately observes its outcome, and sends a cheap-talk message to a receiver. We provide an algorithm valid for arbitrary state-dependent preferences that will determine the sender's optimal experiment and his equilibrium payoff under binary state space. We give sufficient conditions for informative information transmission. These conditions depend more on marginal incentives---how payoffs vary with the state---than on the alignment of sender's and receiver's rankings over actions within a state. The algorithm can be easily modified to study the canonical cheap talk game with a perfectly informed sender.
Archived
Optimal Experiment with Private Repetition (with Zheng Gong)
Abstract: We study a persuasion game with limited commitment in which a biased sender designs and conducts costly experiments to acquire information which he can conceal or reveal. The sender commits to the experiment design, but he can secretly repeat experiments and selectively report the outcomes. In the benchmark model, the optimal experiment turns out to be a one-round experiment and the sender truthfully discloses the experiment outcome. The cost of an experiment is a measure of credibility. Higher credibility leads to less informative experiment which lowers the receiver's payoff. With general payoff function of the sender, the above results remain with mild restrictions. We geometrically characterize the optimal experiment using the same concavification with Kamenica and Gentzkow (2011) but within a refined belief space.
Abstract: We study a persuasion game with limited commitment in which a biased sender designs and conducts costly experiments to acquire information which he can conceal or reveal. The sender commits to the experiment design, but he can secretly repeat experiments and selectively report the outcomes. In the benchmark model, the optimal experiment turns out to be a one-round experiment and the sender truthfully discloses the experiment outcome. The cost of an experiment is a measure of credibility. Higher credibility leads to less informative experiment which lowers the receiver's payoff. With general payoff function of the sender, the above results remain with mild restrictions. We geometrically characterize the optimal experiment using the same concavification with Kamenica and Gentzkow (2011) but within a refined belief space.