Research

Abstract: Consider a Bayesian persuasion problem with one sender and one receiver. If the sender is restricted to sending only verifiable messages, are they strictly worse off than under the optimal information structure with unverifiable messages? We show that the answer is no if and only if, there exists an optimal distribution of posterior beliefs in the Bayesian persuasion problem under which, (i) the support of the distribution is smaller than the number of states, and (ii) a condition we call “pooling verifiability" is satisfied. Specifically, we show that whenever the number of receiver actions is weakly less than the number of states, requiring that messages be verifiable does not hurt the sender. We provide an example with two states and three receiver actions to show that when the optimal distribution of posteriors under general Bayesian persuasion includes two beliefs that both have full support, a restriction to verifiable messages has bite, and the sender is strictly worse off than under Bayesian persuasion.

Abstract: Why do firms rarely use observable output to evaluate employees? This paper explores  evaluation contracts that allow firms to commit to evaluation schemes and compensate employees on evaluations in a dynamic principal-agent setting. We show that introducing evaluations allows the principal to implement stochastic efforts,  mitigating the inefficiencies of punishing the agent for low outputs. As evaluation contracts provide more flexibility in the timing of resolving uncertainties, they are always weakly better than stochastic output-contingent contracts. However, these benefits rely on dynamic interactions and the agent's risk aversion; they disappear when the agent is risk-neutral or in static settings. 

Abstract: Consider a setting where a sender can communicate privately with multiple receivers before they interact. If the equilibrium selection is not the sender-preferred one, standard approaches that focus on the sender recommending actions can be suboptimal. We study how to persuade interacting receivers under equilibrium selections that may differ from the sender-preferred selection. We model the equilibrium selection as an exogenous mechanism that selects receivers’ best responses according to their conjectures. It provides a flexible framework for describing various equilibrium selections in the literature. Our main result characterizes the conditions on primitives for when the sender can coarsen information based on countable partitions of conjectures and recommend the receiver’s equilibrium action and location on that partition without changing the outcome. This result supports a generalized direct approach to compute optimal information structures under nontrivial equilibrium selections. We demonstrate its usefulness in an application with the sender-worst selection.

Abstract: We consider a setting where one sender can communicate with several privately informed receivers through a persuasion mechanism before the receivers play a game. We show that for any potentially randomized persuasion mechanism, under certain conditions, there is an effectively equivalent deterministic persuasion mechanism, and these two mechanisms have the same set of equilibria. We exhibit the usefulness of our result in a new application, where our technique helps to derive the optimal persuasion mechanism. Overall, this paper provides a rationale for the fact that persuasion mechanisms are often deterministic in practice.

Abstract: This paper studies Bayesian games with general action spaces, correlated types and interdependent payoffs. We introduce the condition of ``decomposable coarser payoff-relevant information'', and show that this condition is both sufficient and necessary for the existence of pure-strategy equilibria and purification from behavioral strategies. As a consequence of our purification method, a new existence result on pure-strategy equilibria is also obtained for discontinuous Bayesian games. Illustrative applications of our results to oligopolistic competitions and all-pay auctions are provided.  

Abstract: This paper studies pure strategy perfect and proper equilibria for games with non-atomic measure spaces of players and infinitely many actions. A richness condition (nowhere equivalence) on the measure space of players is shown to be both necessary and sufficient for the existence of such equilibria. The limit admissibility of perfect and proper equilibria is also proved.