  We study environments in which agents are randomly matched to play a
Prisoner's Dilemma, and each player observes a few of the partner's past
actions against previous opponents. We depart from the existing related
literature by allowing a small fraction of the population to be commitment
types. The presence of committed agents destabilizes previously proposed
mechanisms for sustaining cooperation. We present a novel intuitive combination
of strategies that sustains cooperation in various environments. Moreover, we
show that under an additional assumption of stationarity, this combination of
strategies is essentially the unique mechanism to support full cooperation, and
it is robust to various perturbations. Finally, we extend the results to a
setup in which agents also observe actions played by past opponents against the
current partner, and we characterize which observation structure is optimal for
sustaining cooperation.
