Relaxing Common Belief for Social Networks

TL;DR

This paper introduces factional belief, a relaxed form of common belief, to better analyze strategic coordination and revolts in social networks, providing new algorithms and structural insights.

Contribution

It proposes factional belief as a more flexible framework for social network analysis and develops an efficient algorithm for equilibrium characterization in revolt games.

Findings

Factional belief extends common belief to social networks.

An efficient algorithm characterizes possible equilibria.

Structural results inform strategic coordination analysis.

Abstract

We propose a relaxation of common belief called factional belief that is suitable for the analysis of strategic coordination on social networks. We show how this definition can be used to analyze revolt games on general graphs, including by giving an efficient algorithm that characterizes a structural result about the possible equilibria of such games. This extends prior work on common knowledge and common belief, which has been too restrictive for use in understanding strategic coordination and cooperation in social network settings.