Disclosure Games with Large Evidence Spaces

TL;DR

This paper analyzes a disclosure game with large evidence spaces, characterizing equilibrium strategies where the sender selectively discloses evidence to persuade the receiver about the state, including a general framework for such games.

Contribution

It introduces a comprehensive framework for disclosure games with large evidence spaces and characterizes the unique equilibrium value function.

Findings

Seemingly sub-optimal disclosures can be equilibrium strategies.

Disclosures maximize the difference between good and bad signals.

A method to construct equilibria in broad classes of disclosure games.

Abstract

We study a disclosure game with a large evidence space. There is an unknown binary state. A sender observes a sequence of binary signals about the state and discloses a left truncation of the sequence to a receiver in order to convince him that the state is good. We focus on truth-leaning equilibria (cf. Hart et al. (2017)), where the sender discloses truthfully when doing so is optimal, and the receiver takes off-path disclosure at face value. In equilibrium, seemingly sub-optimal truncations are disclosed, and the disclosure contains the longest truncation that yields the maximal difference between the number of good and bad signals. We also study a general framework of disclosure games which is compatible with large evidence spaces, a wide range of disclosure technologies, and finitely many states. We characterize the unique equilibrium value function of the sender and propose a method to construct equilibria for a broad class of games.