  Both conventional wisdom and empirical evidence suggests that arranging a
prior commitment or agreement before an interaction enhances the chance of
reaching mutual cooperation. Yet it is not clear what mechanisms can promote
the participation in and compliance with such a commitment, especially when the
former is costly and deviating from the latter is profitable. Prior work either
considers regimented commitments where compensation is assumed enforceable from
dishonest committers, or assume implicit commitments from every individual (so
they are all in and thus being treated as such). Here we develop a theory of
participation and compliance with respect to an explicit prior commitment under
institutional incentives where individuals, at first, decide whether or not to
join a cooperative agreement to play a one-shot social dilemma game. Using a
mathematical model, we determine when participating in a costly commitment and
complying with it, is an evolutionary stable strategy (ESS) when playing
against all other possible strategies, and results in high levels of
cooperation in the population. We show that, given a sufficient budget for
providing incentives, reward of commitment compliant behaviours better promotes
cooperation than punishment of non-compliant ones. Moreover, by sparing part of
this budget for rewarding those who are willing to participate in a commitment,
the overall frequency of cooperation can be significantly enhanced, for both
reward and punishment. Finally, we find that, surprisingly, the presence of
errors in a participation decision favours evolutionary stability of commitment
compliant strategies and higher levels of cooperation.
