Bayesian Persuasion Research Articles

Competitive Information Disclosure by Multiple Senders

We analyze a model of competition in Bayesian persuasion in which multiple symmetric senders vie for the patronage of a receiver by disclosing information about their respective proposal qualities. We show that a symmetric equilibrium exists and is unique. We then show that as the number of senders increases, each sender discloses information more aggressively; and full disclosure by each sender arises in the limit of infinitely many senders.

A model of Bayesian persuasion with transfers

We analyze a persuasion game in which a sender wants to persuade a receiver to take an action. The sender first produces information about the benefits of taking the action and then offers monetary transfers to the receiver. We characterize a sender-optimal information structure and show that limiting monetary payments may incentivize the sender to produce more information.

A Model of Bayesian Persuasion with Transfers

We analyze a persuasion game in which a sender wants to persuade a receiver to take an action. The sender first produces information about the benefits of taking the action and then offers monetary transfers to the receiver. We characterize a sender-optimal information structure and show that limiting monetary payments may incentivize the sender to produce more information.

Using Cheap Talk to Polarize or Unify a Group of Decision Makers

We develop a model of strategic information transmission from an expert with informational superiority to decision makers who vote on a proposal. We show that an expert’s simple cheap talk strategy can be surprisingly effective in persuading decision makers by polarizing or unifying their opinions. After observing the expert’s cheap talk message, decision makers may ignore their private information and vote according to the expert’s interest, even though they know the expert has her own bias. In other words, the expert’s cheap talk prevents a voting procedure from aggregating decision makers’ private information. We also discuss how our main results extend to a model of Bayesian persuasion.

Test design under voluntary participation

An agent who is imperfectly informed about his binary quality can voluntarily participate in a test that generates a public signal. I study the design of the test that allows for optimal learning of the agent's quality when the agent strives for a high perception of his quality but is averse towards perception risk. For a large class of reduced-form utility functions that reflect these properties, the optimal test is binary and not subject to false positives. I uncover the forces that drive this result and show how the problem with endogenous participation can be transformed into a problem to that the concavification approach from the Bayesian persuasion literature applies. Furthermore, for a non-reduced version of my model where the designer estimates the agent's quality but suffers either more from false positives or from false negatives, I show that the same type of test is optimal.

Bayesian persuasion with multiple senders and rich signal spaces

A number of senders with no ex ante private information publicly choose signals whose realizations they observe privately. Senders then convey verifiable messages about their signal realizations to a receiver who takes a non-contractible action that affects the welfare of all players. The space of available signals includes all conditional distributions of signal realizations and allows any sender to choose a signal that is arbitrarily correlated with signals of others. We characterize the information revealed in pure-strategy equilibria and show that greater competition tends to increase the amount of information revealed.

Persuading the Principal to Wait

We study a Bayesian persuasion game in the context of real options. The Sender (firm) chooses signals to reveal to the Receiver (regulator) each period but has no long-term commitment power. The Receiver chooses when to exercise the option, affecting welfare of both parties. When the Sender favors late exercise relative to the Receiver but their disagreement is small, in the unique equilibrium information is disclosed discretely with a delay and the Receiver sometimes ex-post regrets waiting too long. When disagreement is large, the Sender, instead of acquiring information once and fully, pipets good information over time. These results shed light on the post-market surveillance practices of medical drugs and instruments by the FDA, and the role of pharmaceutical companies in keeping marginally beneficial drugs in the market. When the Sender favors early exercise, the lack of commitment not to persuade in the future leads to unraveling, in equilibrium all information is disclosed immediately. In sharp contrast to static environments, the ability to persuade might hurt the Sender.

Bayesian Persuasion and Moral Hazard

We consider a three-player Bayesian persuasion game in which the sender designs a signal about an unknown state of the world, the agent exerts a private effort that determines the distribution of the underlying state, and the receiver takes an action after observing the signal and its realization. The sender must not only persuade the receiver to select a desirable action, but also incentivize the agent’s effort. We develop a general method of characterizing an optimal signal in this environment. We apply our method to derive concrete results in several natural examples and discuss their economic implications

Divide and Inform: Rationing Information to Facilitate Persuasion

ABSTRACTThis paper develops a Bayesian persuasion model that examines a manager's incentives to gather information when the manager can disseminate this information selectively to interested parties (“users”) and when the objectives of the manager and the users are not perfectly aligned. The model predicts that if the manager can choose the subset of users to receive the information, then the manager may gather more precise information. The paper identifies conditions under which a regime that allows managers to grant access to information selectively maximizes aggregate information. Strikingly, this happens when the objectives of managers and users are sufficiently misaligned. This finding is robust to variations of the model, such as information acquisition cost, unobservable precision, sequential noisy actions taken by the users, and delayed choice of the subset of users in “the know.” These results call into doubt the common belief that forcing managers to provide unrestricted access to information to all potential users is always beneficial.

Information Design: A Unified Perspective

Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures.

Information Design: A Unified Perspective

Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures.

Optimal Signaling Mechanisms in Unobservable Queues

We consider the problem of optimal information sharing in an unobservable single-server queue offering service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider observes the queue, and may share state information with arriving customers. The customers are Bayesian and strategic, and incorporate this information into their beliefs before deciding whether to join the queue. We pose the following question: which signaling mechanism should the service provider adopt to maximize her expected revenue? We formulate this problem as an infinite linear program in the queue's steady-state distribution, and establish that, in general, the optimal signaling mechanism requires the service provider to strategically conceal information in order to incentivize customers to join. In particular, we show that a binary signaling mechanism with a threshold structure is optimal. Finally, we prove that coupled with an optimal fixed price, the optimal signaling mechanism generates the same expected revenue as the optimal state-dependent pricing mechanism. This suggests that in settings where state-dependent pricing is infeasible, signaling can be effective in achieving the optimal revenue. Our work contributes to the literature on dynamic Bayesian persuasion, and provides many interesting directions for extensions.

Limited capacity in project selection: competition through evidence production

An organization must decide which of two proposals to fund. In evaluating the proposals, the organization relies on the agents applying for funding to produce evidence about the merits of their own proposals. When the organization can fund all proposals, each agent engages in an independent game of Bayesian persuasion with the organization, choosing information strategies that maximize the probability of producing evidence in favor of funding. When the organization has limited capacity to implement proposals, the game becomes one of competitive Bayesian persuasion. Producing favorable evidence is not enough to secure funding; an agent must also produce more-favorable evidence than the other agent. We show that an organization’s limited capacity leads agents to produce more (Blackwell) informative evidence than they do when the organization is unconstrained. We fully characterize the unique equilibrium under unlimited and limited capacity, and show that unless the prior strongly favors accepting both proposals, the funding organization is better off when its capacity is limited. The analysis highlights similarities between competitive Bayesian persuasion games and all-pay auctions and generalized Colonel Blotto games.

Bayesian persuasion by a privately informed sender

This paper introduces private sender information in a game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing differences related to the precision of signals and use these to characterize the set of equilibria selected by the D1 criterion. These equilibria are either separating (i.e., the sender's choice of signal reveals his private information to the receiver) or fully disclosing (i.e., the outcome of the sender's chosen signal fully reveals the payoff-relevant state). Which of these two cases occurs is determined by the optimality properties of fully disclosing signals. If full disclosure is optimal for all sender types, then the equilibrium is fully disclosing. Otherwise, the equilibrium is fully separating, and incentive compatibility requires the sender to use signals that are strictly more informative than the ones that would be used under symmetric information. Therefore, when full disclosure is suboptimal, the sender incurs a cost in comparison to the symmetric information case, whereas the receiver benefits from better information.

The optimal disclosure policy in contests with stochastic entry: A Bayesian persuasion perspective

Following a Bayesian persuasion approach, we establish that full disclosure (resp. concealment) is the contest organizer’s effort-maximizing policy for disclosing the number of actual contestants if the characteristic function of the imperfectly discriminatory contest technology is strictly concave (resp. convex).

Bayesian persuasion with heterogeneous priors

In a world in which rational individuals may hold different prior beliefs, a sender can influence the behavior of a receiver by controlling the informativeness of an experiment (public signal). We characterize the set of distributions of posterior beliefs that can be induced by an experiment, and provide necessary and sufficient conditions for a sender to benefit from persuasion. We then provide sufficient conditions for the sender to benefit from persuasion for almost every pair of prior beliefs, even when there is no value of persuasion under a common prior. Our main condition is that the receiver's action depends on his beliefs only through his expectation of some random variable.

Optimal Reporting Systems with Investor Information Acquisition

This paper analyzes a manager’s optimal ex-ante reporting system using a Bayesian persuasion approach (Kamenica and Gentzkow (2011)) in a setting where investors affect cash flows through their decision to finance the firm’s investment opportunities, possibly assisted by the costly acquisition of additional information (inspection). I examine how the informativeness and the bias of the optimal system are determined by investors’ inspection cost, the degree of incentive alignment between the manager and investors, and the prior belief that the project is profitable. I find that a mis-aligned manager’s system is informative only when the market prior is pessimistic and is always positively biased. As investors’ inspection cost decreases, this bias decreases and the optimal system becomes more conservative. In contrast, a well-aligned manager’s system is fully revealing when investors’ inspection cost is high, and is counter-cyclical to the market belief when the inspection cost is low: It is positively (negatively) biased when the market belief is pessimistic (optimistic). I explore the extent to which the results generalize to a case with managerial manipulation and discuss the implications for investment efficiency. Overall, the analysis describes the complex interactions among determinants of firm disclosures and governance, and offers explanations for the mixed empirical results in this area.

Information Disclosure in Contests: A Bayesian Persuasion Approach

We examine optimal information disclosure through Bayesian persuasion in a two-player contest. One contestant's valuation is commonly known and the other's is his private information. The contest organiser can precommit to a signal to in uence the uninformed contestant's belief about the informed contestant. We show that to search for the optimal signal when the informed contestant's valuation follows a binary distribution, it is without loss of generality to compare no disclosure with full disclosure; otherwise, such a restriction causes loss of generality. We propose a simple method to compute the optimal signal, which yields explicit solutions in some situations.

The Simple Economics of Optimal Persuasion

We propose a price-theoretic approach to Bayesian persuasion by establishing an analogy between the sender’s problem and finding Walrasian equilibria of a persuasion economy. The sender, who acts as a consumer, purchases posterior beliefs at their prices using the prior distribution as her endowment. A single firm has the technology to garble the state. Welfare theorems provide a verification tool for optimality of a persuasion scheme and characterize the structure of prices that support the optimal solution. This approach yields a tractable solution method for persuasion problems in which the sender’s utility depends only on the expected state.

Bayesian Persuasion in Coordination Games

We analyze a coordination game of regime change where the policy maker, who tries to increase the probability of the survival of the regime, commits ex ante to abandon the regime automatically when its fundamentals are below a certain threshold. This policy acts as an information transmission mechanism: agents, who decide whether to attack the regime or not, update positively about the fundamentals of the regime when they see that it has not been abandoned, and so they are less likely to attack. Using the commitment ability, the policy maker can thus increase the overall survival probability of the regime.