Optimal Information Structure Research Articles

Dynamic Persuasion and Strategic Search

Consumers frequently search for information before making decisions. Because their search and purchase decisions depend on the information environment, firms have a strong incentive to influence it. This paper endogenizes the consumer’s information environment from the firm’s perspective and endogenizes the search decision from the consumer’s perspective. We consider a dynamic model where a firm sequentially persuades a consumer to purchase the product. The consumer only wishes to buy the product if it is a good match. The firm designs the information structure. Given the endogenous information environment, the consumer trades off the benefit and cost of information acquisition and decides whether to search for more information. Given the information acquisition strategy of the consumer, the firm trades off the benefit and cost of information provision and determines how much information to provide. This paper characterizes the optimal information structure under a general signal space. We find that the firm only smooths information provision over multiple periods if the consumer is optimistic about the product fit before searching for information. Moreover, if the search cost for the consumer is high, the firm designs the information such that the consumer will be certain that the product is a good match and will purchase it after observing a positive signal. If the search cost is low, the firm provides noisy information such that the consumer will be uncertain about the product fit but will still buy it after observing a positive signal. This paper was accepted by Dmitri Kuksov, marketing. Funding: This work was supported by University of California, Berkeley, the Institute for Business Innovation [Research Grant], and the Center for Equity, Gender, and Leadership [Research Grants]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.00994 .

Information design in optimal auctions

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private values. Assuming that the seller adopts the optimal auction due to Myerson (1981) in response, we characterize both the buyer-optimal information structure, which maximizes the buyers' surplus, and the seller-worst information structure, which minimizes the seller's revenue. We translate both information design problems into finite-dimensional, constrained optimization problems in which one can explicitly solve for the optimal information structure. In contrast to the case with one buyer (Roesler and Szentes, 2017), we show that with two or more buyers, the symmetric buyer-optimal information structure is different from the symmetric seller-worst information structure. The good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both symmetric information structures converge to no disclosure. We also show that in our ex ante symmetric setting, an asymmetric information structure is never seller-worst but can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.

Optimal information structures in bilateral trade

With the goal of maximizing expected gains from trade, this paper analyzes the jointly optimal information structure and mechanism in a bilateral trade setting. The difference in gains from trade between the optimal information structure and first best constitutes the minimal loss due to asymmetric information. With binary underlying types it is shown that more than 95% of first best can be achieved while the optimal mechanism without information design may achieve less than 90% of first best. For more general type distributions, the optimal information structure is a monotone partition of the type space and the optimal mechanism is deterministic. Necessary conditions for the optimal information structure are derived and a closed form solution is given for the binary type case.

Global manipulation by local obfuscation

We study adversarial information design in a regime-change context. A continuum of agents simultaneously chooses whether to attack the current regime. The attack succeeds if and only if the mass of attackers outweighs the regime's strength. A designer manipulates information about the regime's strength to maintain the status quo. Our optimal information structure exhibits local obfuscation: some agents receive a signal matching the regime's true strength, and others receive an elevated signal professing slightly higher strength. This policy is the unique limit of finite-signal problems. Public signals are strictly suboptimal, and in some cases where public signals become futile, local obfuscation guarantees the collapse of agents' coordination, making the designer's information disclosure time consistent and relieving the usual commitment concern.

Collective Information Acquisition

Abstract We consider the problem faced by a group of players who bargain over what public signal to acquire before deciding on a collective action. The players differ in their privately known state-dependent payoffs from taking the action, and therefore differ also in their willingness to pay for the public signal. We take a mechanism design approach to characterizing the efficient frontier of outcomes achievable via bargaining over information. We identify novel distortions in the optimal information structure that arise from the information asymmetry and from the fact that after the signal is realized, the outcome is determined in equilibrium of a subsequent voting game.

Multivariate Rational Inattention

We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.

Information design in competitive insurance markets

This paper characterizes the optimal information structure in competitive insurance markets with adverse selection. We consider a regulator that assigns ratings to individuals according to their expected costs. Insurers observe these ratings and compete as in Akerlof (1970). The optimal rating system minimizes ex-ante risk subject to participation constraints. We prove that in any such market there exists a unique optimal system under which all individuals trade and the ratings match low-cost types with high-cost types negative assortatively. We provide a simple algorithm that yields the optimal system and examine implications for government regulations of insurance markets.

Robust persuasion of a privately informed receiver

This paper studies robust Bayesian persuasion of a privately informed receiver in a binary environment, where an ambiguity-averse sender with a maxmin expected utility function has limited knowledge about the receiver’s private information source. We develop a novel method to solve the sender’s information design problem. Our main result shows that the sender’s optimal information structure can be found within the class of linear-contingent-payoff information structures. We also fully characterize the sender’s optimal linear-contingent-payoff information structure and analyze the impact of ambiguity on the sender’s payoff.

On Information Design with Spillovers

An information designer has access to a set of experiments and decides which of these to assign to each of the agents in a directed network. The network encodes informational spillovers: an agent has access to the experiments assigned to her, as well as to those assigned to any other agent who has a directed path to her. We establish that the designer's problem in any network can be reduced to an equivalent problem in a directed acyclic network. We show that when in the latter network each agent follows at most one other agent (i.e., each node has in-degree at most one), the optimal information structure can be obtained in a tractable way. The problem becomes intractable if some agents follow multiple other agents. Thus, qualitatively, following multiple information sources is what makes information design problems intractable in the presence of spillovers. We also study a voting game with binary actions in the presence of spillovers. We show that when the followers are more pessimistic (i.e., have higher posterior mean requirements to take action $1$), the network effects do not play a role, and a certain monotone information structure is optimal. When the followers are more optimistic a monotone information structure is still optimal if each agent follows at most one other agent, but not in general. That said, in the latter case an optimal monotone information structure can be obtained in a tractable way by using an algorithm we provide, provided that the underlying network has bounded treewidth.

Persuasion with Limited Signal Spaces

Communication between parties is an important part of persuasion and the diffi- culty of communication has a first order effect on the outcomes of strategic persuasion games and welfare of agents. We study a model of Bayesian Persuasion in which the communication between the sender and the receiver is coarse, which we model by al- lowing the cardinality of the signal space to be less than the cardinality of the action space and the state space. This limits the number of action recommendations that the sender can make. We define the set of simple Bayes Plausible information structures and show that there exists an optimal information structure that is simple for a signal space with arbitrary finite cardinality. We characterize the set of highest attainable payoffs for any cardinality of the signal space k, by what we call k-concavification of the sender utility. Under coarse communication, sender’s willingness to pay for an ad- ditional signal can be interpreted as the value of precise communication for the sender. We provide an upper bound on the value of precision. While increased precision is always better for the sender, we show that the receiver may prefer coarse communi- cation. We show this by analyzing a game of advice seeking, where the receiver can choose the cardinality of the signal space and ask for simple recommendations.

Information Design

A designer commits to a signal distribution that is informative about a payoff-relevant state. Conditional upon the privately observed signals, agents take actions that affect their payoffs as well as those of the designer. We show how to derive the (designer) optimal information structure in static finite environments. We fully characterize it in a symmetric binary setting for a parameterized game. In this environment, conditionally independent private signals are never strictly optimal. (JEL C72, D78, D82, D83)

Global Manipulation by Local Obfuscation: Information Design in Coordination Games

We study information design in a regime change context. A continuum of agents choose independently whether to attack the current regime and will succeed if and only if the mass of attackers outweighs the regime's strength. The strength is uncertain, and the information designer chooses a strength-dependent experiment to maintain the status quo. The optimal information structure randomizes between partial truth-telling and local exaggeration across agents: some agents receive a signal matching the true strength of the status quo, and others receive an elevated signal professing slightly higher strength. Optimal local obfuscation strictly dominates public signals, and in certain cases where public signals become futile, local obfuscation still guarantees the status quo's survival.

Information control in the hold‐up problem

AbstractWe study the use of information control to mitigate hold‐up risks. We identify a distinction between asymmetric information that creates an ex ante investment incentive and asymmetric information that causes ex post inefficiency, which then allows ex post inefficiency to be eliminated without compromising the ex ante investment incentive. We characterize the properties of the optimal information structure and the payoffs and welfare achievable with information control in the presence of hold‐up risks.

Information and Communication in Organizations

We study a constrained information design problem in an organization. A designer chooses the information structure. A sender with preferences different from the decision-maker observes and processes the information before he communicates with the decision-maker. Information shapes conflicts within the organization: the optimal information structure essentially eliminates conflicts and serves as a substitute to the allocation of decision-making authority in the organization.

Information Control in the Hold-Up Problem

We study the use of information control to mitigate hold-up risks. We identify a distinction between asymmetric information that creates an ex-ante investment incentive and asymmetric information that causes ex-post inefficiency, which then allows ex-post inefficiency to be eliminated without compromising the ex-ante investment incentive. We characterize the properties of the optimal information structure and the payoffs and welfare achievable with information control in the presence of hold-up risks.

Sourcing Innovation: On Feedback in Contests

It is notoriously difficult to provide outside parties with adequate incentives for innovation. Contests—in which solvers compete for a prize offered by the contest holder—have been shown to be an effective incentive mechanism. Despite considerable interest in this concept, we lack a thorough understanding of important aspects of contests; in particular, feedback from the contest holder to the solvers has received only limited attention. This paper discusses how contest holders can improve contest outcomes by devising an optimal information structure for their feedback policies. We first identify when, and when not, to give feedback as well as which type of feedback to give: public (which all solvers can observe) or private (which only the focal solver can observe). We uncover a nontrivial relationship between contest characteristics and optimal feedback choices. Second, we examine whether the contest holder should mandate interim feedback or instead allow solvers to seek feedback at their own discretion. Third, we discuss how changing the granularity of feedback information affects its value to solvers.This paper was accepted by Ashish Arora, entrepreneurship and innovation.

Pivotal persuasion

A sender seeks to persuade a group of heterogeneous voters to adopt an action. We analyze the sender's information-design problem when the collective decision is made through a majority vote and voting for the action is personally costly. We show that the sender can exploit the heterogeneity in voting costs by privately communicating with the voters. Under the optimal information structure, voters with lower costs are more likely to vote for the sender's preferred action when it is the wrong choice than those with higher costs. The sender's preferred action is therefore adopted with a higher probability when private communication is allowed than when it is not. Nevertheless, the sender's preferred action cannot be adopted with probability one if no voter, as a dictator, is willing to vote for it without being persuaded.

Persuasion in Networks: Public Signals and k-Cores

We consider a setting where agents in a social network take binary actions, which exhibit local strategic complementarities. The agents are a priori uninformed about an underlying payoff-relevant state. An information designer wants to maximize the expected number of agents who take action 1, and she can commit to a signaling mechanism which upon the realization of the state sends an informative signal to all the agents. We study the structure and design of the optimal public signaling mechanisms. We establish that given a signal realization, the set of agents who take action 1 correspond to a k-core of the underlying network, for some k. Using this we show that the designer’s payoff is an increasing step function of the posterior mean her signals induce. We provide a convex optimization formulation and an algorithm that obtain the optimal information structure whenever the designer’s payoff exhibits this structure. The latter structural property is prevalent, thereby making our approach useful well beyond network persuasion. The optimal mechanism is based on a double-interval partition of the set of states. In particular, it associates up to two subintervals of the set of possible state realizations with each k-core. When the state is in these intervals the mechanism publicly reveals this, which induces the agents in k-core to take action 1. We also study a class of random networks with known limiting degree distributions, and provide a framework for obtaining asymptotically optimal public signaling mechanisms for these networks. Our approach relies on characterizing the sizes of the cores of such networks (asymptotically) and uses only the degree distribution of the random networks, thereby making it useful even when the network structure is not fully known. Finally, we explore which networks are more amenable to persuasion, and show that more assortative connection structures lead to larger payoffs for the designer. On the other hand, the dependence of the designer’s payoff to the agents’ degrees can be quite counterintuitive. In particular, we focus on networks sampled uniformly at random from the set of all networks consistent with a degree sequence. We show that when the degrees of some nodes increase, this can reduce the designer’s payoff, despite the increase in the extent of the network externalities.

On the hardness of designing public signals

We use computational complexity as a lens to study the design of information structures in games of incomplete information. We focus on one of the simplest instantiations of the information structure design problem: Bayesian zero-sum games, and a principal who must design a public signal maximizing the equilibrium payoff of one of the players. In this setting, we show that optimal information structure design is computationally intractable, and in some cases hard to approximate, assuming that it is hard to recover a planted clique from an Erdős–Rényi random graph. Our result suggests that there is no “simple” characterization of optimal public-channel information structures in multi-player settings.

The Benefit of Collective Reputation

We study a model of collective reputation and use it to analyze the benefit of collective brands. Consumers form beliefs about the quality of an experience good that is produced by one firm that is part of a collective brand. Consumers’ limited ability to distinguish among firms in the collective and to monitor firms’ investment decisions creates incentives to free-ride on other firms’ investment efforts. Nevertheless, we show that collective brands induce stronger incentives to invest in quality than individual brands under two types of circumstances: if the main concern is with quality control and the baseline reputation of the collective is low, or if the main concern is with the acquisition of specialized knowledge and the baseline reputation of the collective is high. We also contrast the socially optimal information structure with the profit maximizing choice of branding if branding is endogenous. Our results can be applied to country-of-origin, agricultural appellation, and other collective brands.