Monday

9h30 Welcome

9h45-10h30 Françoise Forges

Title : Strategic information transmission with sender's approval (joint with Jérôme Renault)

Abstract :

We consider a sender-receiver game with finitely many types for the sender. After the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject in favor of an outside option. We assume that the sender's approval is crucial to the receiver. A subgame perfect equilibrium (SPNE) with sender's approval is characterized by two sets of conditions: incentive compatible splitting and constrained optimization. We ask whether such a SPNE exists.

We construct a counter-example (with three types for the sender and type-dependent affine utility functions) in which there is no mixed SPNE, but there is a communication equilibrium.

We show that a pure SPNE exists under various assumptions, for instance if the sender has only two types or if the receiver’s preferences over decisions do not depend on the type of the sender as long as the latter participates.

We show that a communication equilibrium always exists when the sender has three types and the utility functions are affine.

Coffee Break

11h00-11h45 Laurent Mathevet

Title : Attention management (joint with E. Lipnowski and D. Wei)

Abstract :

Attention costs can cause some information to be ignored and deci- sions to be imperfect. Can we improve the material welfare of a rationally inattentive agent by restricting his information in the first place? In our model, a well-intentioned principal provides information to an agent for whom information is costly to process, but the principal does not internalize this cost. We show that full information is universally optimal if and only if the environment comprises one issue. With multiple issues, attention management becomes optimal: the principal restricts some information to induce the agent to pay attention to other aspects.

11h45-12h30 Ina Taneva

Title : Informational Hierarchies (joint with L. Mathevet)

Abstract :

In information design problems with complementarities we show that there is an optimal information structure with a hierarchical property: players can be assigned into groups that are totally ranked with respect to signal informativeness. Compared to direct action recommendations, this information structure has additional properties related to implementation and robustness to limited commitment. The hierarchical structure makes a connection to organisational design and the flow of information in organisations. Under certain conditions the designer benefits from having a new player join the game and we explain where in the hierarchy this player should be introduced.

Lunch

14h00-14h45 Jérôme Renault

Title : Long Information Design (joint with F. Koessler, M. Laclau and T. Tomala)

Abstract :

We study competitive information design games between two designers who want to influence the final action of a decision-maker. Each designer controls the public information on a private persistent state: in each period the designers can disclose information to the decision-maker about their own state. Using tools from repeated games with incomplete information on both sides, we study equilibrium payoffs and strategies depending on the timing of the game and the possible deadline. Our analysis covers continuous environments as well as environments in which designers can only induce finite sets of posterior beliefs: in the latter framework, there may be no bound on the number of communication stages required at equilibrium.

14h45-15h30 Wei Zhao

Title : Contracting over persistent information (joint with T. Tomala and L. Renou)

Abstract :

We consider a dynamic moral hazard problem between a principal and an agent, where the sole instrument the principal has to incentivize the agent is the disclosure of information. The principal aims at maximizing the (discounted) number of times the agent chooses a particular action, e.g., to exert high effort. We show that there exists an optimal contract, where the principal stops disclosing information as soon as its most preferred action is a static best reply for the agent or else continues disclosing information until the agent perfectly learns the principal’s private information.

Coffee Break

16h00-16h45 Penelope Hernandez

Title : How Bayesian Persuasion can Help Reduce Illegal arking and Other Socially Undesirable Behavior (joint with Z. Neeman)

Abstract :

We consider the question of how best to allocate enforcement resources across different locations with the goal of deterring unwanted behaviour. We rely on “Bayesian

persuasion” to improve deterrence. For simplicity, we focus on the problem of how to allocate resources in order to reduce the extent of illegal parking. However, the same

model can also be applied to many other types of socially undesirable behaviour. We show that the problem of how to allocate resources and then “persuade,” can be rep-

resented as a linear programming problem. Notably, optimal persuasion involves the use of only two messages, “high” and “low” that indicate that the amount of expected

resources available is high and low, respectively. However, unlike standard results in Bayesian persuasion, it is only possible to achieve a “partially convex” objective func-

tion. We also obtain a full solution for a class of “monotone” problems.

Tuesday

9h45-10h30 Cédric Langbort

Title : On some models of non-(fully) Bayesian persuasion (joint with S. Nadendla and O. Massicot )

Abstract :

We consider several departures from the Bayesian Persuasion model of Gentzkow & Kamenica (GK) in which the receiver interprets messages in a non-Bayesian way.

In one model, the receiver accurately computes her posterior but, instead of determining her action from expected (with respect to the posterior) utility maximization, optimizes a prospect theory-like value function with deformed subjective probabilities. In the other model, the posterior ends up in an $\epsilon$-neighborhood of the fully Bayesian one, due to errors in the updating process and/or restricted computational resources when performing variational Bayes optimization.

After describing and justifying those models, we study their predictions for the quadratic Gaussian case with noise, which is meaningful in the context of engineering applications and news markets. For the prospect theory-like case, we show that transmission strategies are unaltered with respect to the GK situation, even though the induced belief and utilities are different. In the almost Bayesian case, we show that (1) depending on

closeness of the two utilities, the transmitter either fully reveals the variable of interest or sends no message at all, and (2) that as the receiver becomes increasingly less Bayesian (i.e., as $\epsilon$ increases), the transmitter is increasingly willing to produce a message even as utilities differ.

Coffee Break

11h00-11h45 Serdar Yuksel

Title : Geometry of Information Structures and Strategic Measures (joint work with N. Saldi and S. Sanjari)

Abstract :

This talk is concerned with the geometric properties of information structures in decentralized/multi-agent systems in view of convexity, compactness, existence, and approximation properties. Our primary focus will be on stochastic team problems. We will investigate decentralized strategic measures; these are the probability measures induced on the space of measurement and action sequences under admissible policies/strategies which satisfy various measurability and conditional independence/common randomness properties. Conditions ensuring compactness of various sets of strategic measures will be established under various topologies on sets of probability measures. These will lead to existence results on optimal solutions. Properties such as convexity and Borel measurability of various sets of such measures, and their implications, will be established. We also introduce convex sets of measures obtained by further relaxations on admissible strategic measures (including those known as non-signaling policies in the quantum information theory literature) but that lead to strict lower bounds despite desirable mathematical properties. However, we will show that these measures lead to existence and optimality results for the non-relaxed problem as the number of decision makers approaches infinity under permutation invariant cost criteria, and which further reduce to symmetric, possibly randomized, policies under convex cost criteria with mild conditions. Finally, through a proper approximation of the sets of strategic measures by those induced with quantization of measurement and action spaces, asymptotic optimality of finite state/action model representations for problems with standard Borel spaces will be established.

11h45-12h30 Shaddin Dughmi

Title : Algorithmic Information Structure Design: Two Vignettes, and Lessons Learned.

Abstract :

Classically in economics, the study of how information influences strategic interactions has been largely descriptive. A more recent line of work, which is becoming increasingly relevant in today’s information economy, examines the associated prescriptive question: what information should a system designer communicate to self-interested agents in order to steer their collective behavior towards a desirable outcome. This task, often referred to as persuasion or information structure design, is fundamentally algorithmic in nature, and therefore naturally lends itself to analysis through the computational lens. The computational perspective not only lays the groundwork for application, but also provides structural insights into the underlying economic models.

In this talk, I will provide a brief overview of the field, and present two vignettes from the work in my group on this topic. I will emphasize the structural insights enabled by the computational perspective.

Lunch

14h00-14h45 Rida Laraki

Title : Acyclic Gambling Games (joint with J.Renault)

Abstract :

We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino. Under standard assumptions (e.g. continuous running payoff and non-expansive transitions), we consider for each discount factor the value of the discounted stochastic game and investigate its limit as the discount factor goes to 1 (players are more and more patient). We show that under a new acyclicity condition, the limit exists and is characterized as the unique solution of a system of functional equations: the limit is the unique continuous excessive and depressive function such that each player, if his opponent does not move, can reach the zone when the current payoff is at least as good as the limit value, without degrading the limit value. The approach generalizes and provides a new viewpoint on the Mertens-Zamir system coming from the study of zero-sum repeated games with lack of information on both sides. A counterexample shows that under a slightly weaker notion of acyclicity, convergence of the discounted value may fail.

14h45-15h30 Miquel Oliu-Barton

Title : The Splitting Game has a uniform value

Abstract :

We introduce the dependent splitting game, a zero-sum stochastic game in which the players jointly control a martingale. This game models the transmission of information in repeated games with incomplete information on both sides, in the dependent case: the state variable represents the martingale of posterior beliefs. We establish the following surprising result: unlike repeated game with incomplete information on both sides,

the splitting game has a uniform value. Moreover, we exhibit a couple of optimal stationary strategies for which the stage pay-off and the state remain constant during the play.

Pause Café

16h00-16h45 Maël Le Treust

Title : Persuasion with limited communication capacity (joint with T. Tomala)

Abstract :

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel which has a fixed and limited number of messages and is subject to exogenous noise. Imperfect communication entails a loss of payoff for the persuader. We establish an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight: if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies which tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel

Social Diner (speaker only)

Wednesday

9h45-10h30 Marcin Peski

Title : Alternating offer bargaining with incomplete information

Abstract :

We study an alternating offer bargaining over heterogeneous pie with N parts, and with one-sided uncertainty about the preferences over different parts of the pie. An offer takes form of an arbitrary finite (multi-period) mechanism where action choices determine the division of the pie. When N=2 and offers are frequent, the game has unique equilibrium. The uninformed player proposes the optimal screening menu subject to the constraint that each of the types u of the informed player gets at least her complete information benchmark N\left(u\right). When N>2, there are multiple equilibria. We show that there always is an equilibrium, in which the uninformed player proposes the optimal screening menu subject to the constraint that each of the types u of the informed player gets at least \text{Vex}N\left(u\right).

Coffee Break

11h00-11h45 Laura Doval

Title : Sequential Information Design (joint with Jeffrey C. Ely)

Abstract :

We study games of incomplete information as both the information structure and the extensive form vary. An analyst may know the payoff-relevant data but not the players’ private information, nor the extensive form that gov-erns their play. Alternatively, a designer may be able to build a mechanismfrom these ingredients. We characterize all outcomes that can arise in an equilibrium of some extensive form with some information structure. We showhow to specialize our main concept to capture the additional restrictions implied by extensive-form refinements.

11h45-12h30 Peter Sorensen

Title : Informational Herding, Optimal Experimentation, and Contrarianism. (joint with Lones Smith and Jianrong Tian).

Abstract :

In a standard herding model, individuals sequentially see prior actions and act. An identicalaction herd starts and public beliefs land in “cascade sets” where social learning stops. But actions ignore any informational externality. What behaviour is socially efficient? We fully solve this long open problem, deducing four key findings: (a) cascade sets shrink but do not vanish, and some herding should occur but less readily; (b) it is efficient to reward individuals mimicked by their successor; (c) self-interested cascades cannot start after period one under a simple log-concavity condition; (d) given this condition, contrarian behaviour is efficient in every period — i.e. individuals should optimally lean against taking the myopically more popular actions. The paper introduces generally useful novel methods of monotone comparative statics under uncertainty to characterize optimal dynamic behaviour, and adapts dynamic pivot mechanisms for a Bayesian context.