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.
Coarse Information Design (with Wing Suen and Yimeng Zhang)
October 2023
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; each interval cutoff is the conditional mean (taken under the value function curvature) of the interval formed by neighbouring signals. This property enables examination into which part of the state space is more finely partitioned and facilitates comparative statics analysis. The analysis can be extended to general value functions and adapted to study coarse mechanism design.
An alternative explanation for the dual expectation can be found here!
October 2023
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; each interval cutoff is the conditional mean (taken under the value function curvature) of the interval formed by neighbouring signals. This property enables examination into which part of the state space is more finely partitioned and facilitates comparative statics analysis. The analysis can be extended to general value functions and adapted to study coarse mechanism design.
An alternative explanation for the dual expectation can be found here!
Information Design in Cheap Talk (with Wing Suen)
January 2023
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 give sufficient conditions for information design to be valuable or not under different payoff structures. 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.
You can check the old version here.
January 2023
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 give sufficient conditions for information design to be valuable or not under different payoff structures. 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.
You can check the old version here.
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.