  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.
