Published, Forthcoming and Accepted Papers
A sender commissions a study to persuade a receiver, but influences the report with some probability. We show that increasing this probability can benefit the receiver and can lead to a discontinuous drop in the sender’s payoffs. To derive our results, we geometrically characterize the sender’s highest equilibrium payoff, which is based on the concavification of a capped value function.
We study optimal testing to inform quarantine decisions for a population exhibiting heterogeneous probability of carrying a pathogen. Because test supply is limited, the planner may choose to test a pooled sample, which contains the specimens of multiple individuals (Dorfman, 1943). We characterize the unique optimal allocation of tests. This allocation features assortative batching, whereby agents of differing infection risk are never jointly tested. Moreover, the planner tests only individuals whose prior quarantine decision is most uncertain. Finally, individuals with higher infection risk are tested in smaller batches, because such tests minimize the informational externality of group testing.
This paper analyzes a bilateral trade model where the buyer's valuation for the object is uncertain and she can privately purchase any signal about her valuation. The seller makes a take-it-or-leave-it offer to the buyer. The cost of a signal is smooth and increasing in informativeness. We characterize the set of equilibria when learning is free and show that they are strongly Pareto ranked. Our main result is that, when learning is costly but the cost of information goes to zero, equilibria converge to the worst free-learning equilibrium.
We study a static self-control model in which an agent's preference, temptation ranking, and cost of self-control drive her choices among a finite set of options. We show that it is without loss to assume that the agent's temptation ranking is the opposite of her preference. We characterize the model by relaxing the Weak Axiom of Revealed Preference (WARP), and exploit WARP violations to identify the model's parameters.
A seller bargains with a rationally inattentive buyer (Sims, 2003) over a good of random quality. After observing quality, the seller makes a take-it-or-leave-it offer. The buyer pays attention to the seller's product and offer at a cost proportional to expected entropy reduction. Because attention is free off-path, multiple equilibria emerge, many of which are efficient. A trembling-hand-like refinement (Selten, 1975) rules out efficiency, delivering complete disagreement when attention is expensive and a unique equilibrium with trade when attention is cheap. In this equilibrium, the buyer overpays for low-quality goods, underpays for high-quality goods, and earns a strictly positive payoff.
We study a model of cheap talk with one substantive assumption: The sender’s preferences are state-independent. Our main observation is that such a sender gains credibility by garbling self-serving information. Using this observation, we examine the possibility of valuable communication, assess the value of commitment, and explicitly solve for sender-optimal equilibria in several examples. A key result is a geometric characterization of the value of cheap talk, described by the quasiconcave envelope of the sender’s value function.
Knowing the Informed Player's Payoffs and Simple Play in Repeated Games (with Takuma Habu and Elliot Lipnowski, R&R JET)
We revisit the classic model of two-player repeated games with undiscounted utility, observable actions, and one-sided incomplete information, and further assume the informed player has state-independent preferences. We show the informed player can attain a payoff in equilibrium if and only if she can attain it in the simple class of equilibria first studied by Aumann, Maschler, and Stearns (1968), in which information is only revealed in the game's initial stages. This sufficiency result does not extend to the uninformed player's equilibrium payoff set.
A sender publicly commits to an experiment to inform a receiver's decision. We study attainable sender payoffs, accounting for her incentives at the experiment choice stage, and not presupposing a receiver tie-breaking rule when indifferent. We characterize when the sender has a unique equilibrium payoff, which therefore coincides with her optimal value in Kamenica and Gentzkow (2011). A sufficient condition is that every action which is a receiver best response to some belief over a set of states is a unique best response to some other such belief---a generic property in the finite case.
We study the following random choice procedure. First, the agent focuses on an option at random from the set of available options. Then, she compares the focal option to each other available alternative. Comparisons are binary, random and independent of each other. The agent chooses the focal option if it passes all comparisons favorably. Otherwise, the agent draws a new focal option with replacement. We characterize the procedure's revealed preference implications, show that it accommodates the Attraction effect and Choice overload, and discuss how to conduct welfare comparisons. We conclude by showing that while utility maximization is the procedure's unique deterministic special case, nearly deterministic versions of the procedure can exhibit context effects.