Work-in-Progress
Equilibrium Selection in Cheap Talk Games, with Sidartha Gordon, Navin Kartik, Wojciech Olszewski, and Joel Sobel
Political Career Concerns and Optimal Government Hierarchies, with Yuk-Shing Cheng and Kim-Sau Chung
Selling Multi-dimensional products to Consumers with Intransitive Indifference, with Kim-Sau Chung
Working Papers:
Selling to Consumers with Intransitive Indifference with Kim-Sau Chung and Erica Meixiazi Liu, R&R at JET
We are indifferent between two cups of coffee when one differs from the other in having only one more grain of sugar. But such an indifference is not transitive, because eventually, after many enough grains of sugar are added, we will become able to tell one cup is sweeter than the other. When consumers feature intransitive indifference, putting a bad deal alongside a good deal can boost the sale of the latter by helping consumers to better appreciate it. When sellers compete for these consumers, they tend not to undercut each other, because undercutting often go un-appreciated. Instead, sellers segregate into providers of good deals and bad deals, with the formers free-riding on the latters in helping consumers better appreciate their good deals, and the latters free-riding on the formers in making consumers less hesitant to buy.
We are indifferent between two cups of coffee when one differs from the other in having only one more grain of sugar. But such an indifference is not transitive, because eventually, after many enough grains of sugar are added, we will become able to tell one cup is sweeter than the other. When consumers feature intransitive indifference, putting a bad deal alongside a good deal can boost the sale of the latter by helping consumers to better appreciate it. When sellers compete for these consumers, they tend not to undercut each other, because undercutting often go un-appreciated. Instead, sellers segregate into providers of good deals and bad deals, with the formers free-riding on the latters in helping consumers better appreciate their good deals, and the latters free-riding on the formers in making consumers less hesitant to buy.
Language and Coordination Games R&R at ET
This paper studies pre-game communication of coordination games, where any Sender action and the Receiver's best response forms a nash equilibrium. A pre-existing language is captured by the assumption that the Receiver either ignores or follows the Sender's recommendation, but never inverts it. This assumption alone does not eliminate any equilibrium outcome of the original cheap talk game. However, if the stage game satisfies a self-signaling condition a la Baliga and Morris (2002), then in every iterative admissible outcome, the Sender obtains her Stackelberg payoff. This paper also shows that some form of self-signalling is necessary to guarantee coordination.
This paper studies pre-game communication of coordination games, where any Sender action and the Receiver's best response forms a nash equilibrium. A pre-existing language is captured by the assumption that the Receiver either ignores or follows the Sender's recommendation, but never inverts it. This assumption alone does not eliminate any equilibrium outcome of the original cheap talk game. However, if the stage game satisfies a self-signaling condition a la Baliga and Morris (2002), then in every iterative admissible outcome, the Sender obtains her Stackelberg payoff. This paper also shows that some form of self-signalling is necessary to guarantee coordination.
Rating and Competition Among Information Intermediaries
Because rating agencies are paid by the firms they rate, the industry relies on reputation mechanism to keep conflict of interests in check. If the agency caves in to the pressure to give a bad firm a good rating it does not deserve , the agency obtains short-run benefits, but its reputation will suffer, lowering its future value of business. The two forces are balanced in equilibrium.
We show that competition can weaken reputation mechanism. Good firms are better businesses than bad firms, because giving the good rating that the firm wants does not have repercussion on agency's future reputation. Therefore, agencies compete more fiercely for good firms than for bad firms. Thus competition lowers the margin from good firms more than the margin from bad firms, thereby making short-run gain from lying more important.
Because rating agencies are paid by the firms they rate, the industry relies on reputation mechanism to keep conflict of interests in check. If the agency caves in to the pressure to give a bad firm a good rating it does not deserve , the agency obtains short-run benefits, but its reputation will suffer, lowering its future value of business. The two forces are balanced in equilibrium.
We show that competition can weaken reputation mechanism. Good firms are better businesses than bad firms, because giving the good rating that the firm wants does not have repercussion on agency's future reputation. Therefore, agencies compete more fiercely for good firms than for bad firms. Thus competition lowers the margin from good firms more than the margin from bad firms, thereby making short-run gain from lying more important.
On the Linkage Effect in the Paradigm of Affiliated Signals and Interdependent Values with Art Shneyerov and Pai Xu
When buyer values are interdependent, participation of another bidder reveals positive information and raises the auction price. Such an information channel gives rise to a linkage effect that incentivises the seller to encourage entry. Hence the linkage effect goes in the opposite direction than concern of information rent. It can therefore potentially correct under-provision by monopolists.
We examine the role of linkage effect on the existence and uniqueness of a separating equilibrium when higher reserve price signals more favourable seller information. With affiliated signals, higher seller types believe that buyers tend to have more favourable information as well, leading to a stronger linkage effect. Since linkage effect incentivises the seller to lower the reserve price to encourage entry, but higher seller types must set higher reserve price in a separating equilibrium, we hence show that a separating equilibrium exists when the linkage effect increases with seller's signals at a moderate rate. This is the case when neither value interdependence and signal affiliation is too strong.
When buyer values are interdependent, participation of another bidder reveals positive information and raises the auction price. Such an information channel gives rise to a linkage effect that incentivises the seller to encourage entry. Hence the linkage effect goes in the opposite direction than concern of information rent. It can therefore potentially correct under-provision by monopolists.
We examine the role of linkage effect on the existence and uniqueness of a separating equilibrium when higher reserve price signals more favourable seller information. With affiliated signals, higher seller types believe that buyers tend to have more favourable information as well, leading to a stronger linkage effect. Since linkage effect incentivises the seller to lower the reserve price to encourage entry, but higher seller types must set higher reserve price in a separating equilibrium, we hence show that a separating equilibrium exists when the linkage effect increases with seller's signals at a moderate rate. This is the case when neither value interdependence and signal affiliation is too strong.
Bridging the Preference Gap --- The Function of an Information Intermediary
In an environment where two experts have information on different dimensions relevant for a decision maker, I compare communication through one expert as an intermediary (hierarchical communication) with direct communication from both (independent communication). The intermediary improves decision-making by filtering the sender's information. This filter function is most pronounced when experts share similar preferences, and is irrelevant when they have opposing biases. An optimal intermediary should have a moderate bias.
In an environment where two experts have information on different dimensions relevant for a decision maker, I compare communication through one expert as an intermediary (hierarchical communication) with direct communication from both (independent communication). The intermediary improves decision-making by filtering the sender's information. This filter function is most pronounced when experts share similar preferences, and is irrelevant when they have opposing biases. An optimal intermediary should have a moderate bias.
Common Knowledge of Language and Iterative Admissibility in a Sender Receiver Game
I consider sender receiver games a la Crawford and Sobel (1987). I model a pre-existing common language by assuming that the receiver only plays strategies that satisfy two conditions: (1) the absolute meaning condition: if the receiver responds to any message with a particular action, then that action’s corresponding message also induces it; (2) the convexity condition: if the receiver responds to two messages with the same action, ignoring their literal differences, then the receiver responds to all messages in between the two with the same action. I show that, if the underlying game satisfies a monotonicity condition, then in every outcome of the solution set, the sender can induce at least as many different actions as in the most informative equilibrium. This creates a lower bound on the amount of information transmitted. This stands in sharp contrast babbling equilibrium in which no information is transmitted.
I consider sender receiver games a la Crawford and Sobel (1987). I model a pre-existing common language by assuming that the receiver only plays strategies that satisfy two conditions: (1) the absolute meaning condition: if the receiver responds to any message with a particular action, then that action’s corresponding message also induces it; (2) the convexity condition: if the receiver responds to two messages with the same action, ignoring their literal differences, then the receiver responds to all messages in between the two with the same action. I show that, if the underlying game satisfies a monotonicity condition, then in every outcome of the solution set, the sender can induce at least as many different actions as in the most informative equilibrium. This creates a lower bound on the amount of information transmitted. This stands in sharp contrast babbling equilibrium in which no information is transmitted.