  Tiny perturbations may trigger large responses in systems near criticality,
shifting them across equilibria. Committed minorities are suggested to be
responsible for the emergence of collective behaviors in many physical, social,
and biological systems. Using evolutionary game theory, we address the question
whether a finite fraction of zealots can drive the system to large-scale
coordination. We find that a tipping point exists in coordination games,
whereas the same phenomenon depends on the selection pressure, update rule, and
network structure in other types of games. Our study paves the way to
understand social systems driven by the individuals' benefit in presence of
zealots, such as human vaccination behavior or cooperative transports in animal
groups.
