Coarse Information Design (with Wing Suen and Yimeng Zhang)
May 2024
We study an information design problem with continuous state and discrete signal space. Under convex 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 conditional mean (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.
(The previous alternative explanation for the dual expectation is included in the paper now.)
May 2024
We study an information design problem with continuous state and discrete signal space. Under convex 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 conditional mean (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.
(The previous alternative explanation for the dual expectation is included in the paper now.)
Information Design in Cheap Talk (with Wing Suen)
May 2024
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.
You can check the old version here.
May 2024
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.
You can check the old version here.
Optimal Refund Mechanism with Consumer Learning
April 2024 R&R at RAND
This paper studies the optimal refund mechanism when an uninformed buyer can privately acquire information about his valuation of a product over time. We consider a class of refund mechanisms based on stochastic return policies: if the buyer requests a return, the seller will issue a (partial) refund while allowing the buyer to keep the product with some probability. Such return policies can affect the buyer's learning process and thereby influence the return rate. Nevertheless, we show that the optimal refund mechanism is deterministic and takes a simple form: either the seller offers a sufficiently low price and disallows returns to deter buyer learning, or she offers a sufficiently high price with free returns to implement maximal buyer learning. The form of the optimal refund mechanism is non-monotone in the buyer's prior belief regarding his valuation.
April 2024 R&R at RAND
This paper studies the optimal refund mechanism when an uninformed buyer can privately acquire information about his valuation of a product over time. We consider a class of refund mechanisms based on stochastic return policies: if the buyer requests a return, the seller will issue a (partial) refund while allowing the buyer to keep the product with some probability. Such return policies can affect the buyer's learning process and thereby influence the return rate. Nevertheless, we show that the optimal refund mechanism is deterministic and takes a simple form: either the seller offers a sufficiently low price and disallows returns to deter buyer learning, or she offers a sufficiently high price with free returns to implement maximal buyer learning. The form of the optimal refund mechanism is non-monotone in the buyer's prior belief regarding his valuation.
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.