  Common knowledge of intentions is crucial to basic social tasks ranging from
cooperative hunting to oligopoly collusion, riots, revolutions, and the
evolution of social norms and human culture. Yet little is known about how
common knowledge leaves a trace on the dynamics of a social network. Here we
show how an individual's network properties---primarily local clustering and
betweenness centrality---provide strong signals of the ability to successfully
participate in common knowledge tasks. These signals are distinct from those
expected when practices are contagious, or when people use less-sophisticated
heuristics that do not yield true coordination. This makes it possible to infer
decision rules from observation. We also find that tasks that require common
knowledge can yield significant inequalities in success, in contrast to the
relative equality that results when practices spread by contagion alone.
