Intro to Information Design (and some Basic Bayesian Persuasion) L7

General information Design Two agents: Sender (S) (designer) and Receivers (R) Type space Action space. . Message space Preferences S message strategy Relative to cheap talk: S commits to information structure objective: ex ante welfare of S Players (R), strategies and payoffs, along with define Bayesian game Each BN equilibrium generates unique decision rule Let be a set of equilibrium decision rules in game Solution concept

Remarks Problem can be easily accommodated Adversarial (robust) approach Harder, no revelation principle Gains popularity recently Alternative: receivers with private information Bayesian persuasion problem is a (very) special case One receiver Max max criterion S no private information Type independent preferences of S

Big picture Cheap talk: no commitment power, S and R maximizes ex post welfare Mechanism design (Arbitration) Single receiver (designer), potentially many senders Commitment by R R maximizes ex ante welfare, S welfare ex post Information design (Bayesian Persuasion) Single sender, potentially many receivers Commitment by S S maximizes ex ante welfare, R welfare ex post (with respect to posterior) General mechanism design (Myerson 82)

Senders commitment Sender ex ante commits to message strategy, maximizes ex ante welfare Literal information designer (KG 2011): Legal mandate (a prosecutor and a judge) Coarse grading policies Rating agencies Public tests of the products (medical drug trials) Metaphorical information designer Minimal revenue in auctions (BBM 2017) Maximal volatility of aggregate output (BHM 2017) Welfare outcomes (BBM 2017)

Main lessons Substantive Insights : Conditions for (full or partial) information transmission Obfuscation of information (outcome manipulation) Less power to manipulate if R more informed (more precise prior) Many R: Private vs public signals Technical insights: Concavification of value function Two stage procedure (feasible outcome =correlated equilibrium)

Information Design Literature Discussed papers: Kamienica and Genzkow (AER 2011) Bergmann and Morris (2017) Genzkow and Kamienica (REStud 2017) Other important papers: Bergmann and Morris (ECMA 2013, TE 2016) Mathavet Perego and Taneva (2016) Bergmann Heumann and Morris (JET 2015) Bergmann, Brooks, and Morris (2017) Kolotlin, Mylovanov and Zapechelnyuk (2015)

Dynamic Information Design Papers: Ely (AER 2017) Ely Frankel and Kamienica (JPE 2015) Doval and Ely (2016)

Bayesian persuasion Two agents: Sender (S) and Receiver (R) Type space Action space . Message space Preferences Timing (1) S commits to experiment (2) S observes type, sends message according to distribution (3) R observes message choses action Let Solution: strategy

Example 1: Persuasion in a quadratic model State space Preferences: Fix Best response of R Ex ante welfare of S Optimal persuasion rule:

Example 1: Persuasion in a quadratic model Relative to cheap talk: - No multiplicity of equilibria - S could commit to ``bubbling’’ but in this example it is suboptimal Relative to Arbitration (Mechanism Design) - Commitment benefits more the side that cannot commit Problem more interesting with type independent preferences of S

Example 2: KG example Story: prosecutor S and judge R Binary model Preferences Cheap talk prediction?

Beliefs and expected utility of S Fix R beliefs over types Expected R utility given beliefs R best response given Expected utility as a function of beliefs (no persuasion) Think of S as manipulating ex post beliefs

Example 2: KG example Value function

Information structures Value function

Information structures Value function