Disclosure (Persuasion) games Verifiable Signals L11 Disclosure (Persuasion) games

Papers Milgrom (JEP 2007) Shin (ECMA 2002) Glazer and Rubinstein (ECMA 2004), (TE 2006), Dziuda (JET 2011) Literature on market design

Information Transmission in Markets Cheap Talk literature derives language endogenously (in equilibrium) In markets - meaning of messages already established (quality, emissions level etc.) - conditional on a state, statements are either true and false - legal/institutional framework prevents false statements True reports need not be complete or detailed

Basic Persuasion Game One Sender and one Receiver Timing and actions (no commitment): Sender observes state , , sends message Receiver observes messages. , choses action Preferences: Sender: type independent Receiver: supermodular Exogenous language: message space Verifiable signals (alternative interpretation) Type dependent message space Infinite cost of lying Latter interpretation: a special case of signaling game (a’la Spence)

Example: A seller and a buyer A drug seller (S) and a hospital (R). quality of a drug (survival rate after treatment ) message space = statements ``survival rate is at least ’’ Hospital (R) demand is Seller (S) maximizes quantity If , seller goes to jail forever (and everyone knows it).

PBN Equilibrium Strategies: Sender Receiver Posterior D: Equilibrium s.t. 1. 2. 3.

Bubbling equilibrium?

Refinements for signaling gAmes Many refinements: Intuitive, Devine criterions Weakest: Strict dominance criterion For type message is dominated by if for any type let ``Reasonable’’ (off equilibrium) beliefs satisfy Set of refined PBN equilibria in signaling game set of PBN in a simplified game with state dependent strategy space Persuasion game

Unraveling of information Equilibrium is fully revealing if P: Every dominance refined PBN is fully revealing C: Every PBN equilibrium in a game with type dependent message space is fully revealing Benchmark result

Proof

Proof

Unraveling of information Multiplicity of (outcome equivalent) equilibria Unraveling of information from the top Extreme receiver ‘s skepticism Normative implications: Efficient outcome No room for market regulation