Feasible Conditional Belief Distributions

TL;DR

This paper introduces a new approach to understanding complex belief distributions in multi-agent settings by focusing on their simplified structure when conditioned on the state, enabling more tractable analysis and solutions.

Contribution

It reveals that conditioned belief distributions are constrained only by marginal distributions, leading to new tractable cases in multi-receiver persuasion using optimal transportation and duality.

Findings

Simplified belief structure when conditioned on the state.

Identification of new tractable cases in persuasion problems.

Application of optimal transportation and duality tools.

Abstract

Agents receive private signals about an unknown state. The resulting joint belief distributions are complex and lack a simple characterization. Our key insight is that, when conditioned on the state, the structure of belief distributions simplifies: feasibility constrains only the marginal distributions of individual agents across states, with no joint constraints within a state. We apply this insight to multi-receiver persuasion, identifying new tractable cases and introducing optimal transportation and duality tools.