Evolution of commitment and level of participation in public goods games

Before engaging in a group venture agents may require commitments from other members in the group, and based on the level of acceptance (participation) they can then decide whether it is worthwhile joining the group effort. Here, we show in the context of public goods games and using stochastic evolutionary game theory modelling, which implies imitation and mutation dynamics, that arranging prior commitments while imposing a minimal participation when interacting in groups induces agents to behave cooperatively. Our analytical and numerical results show that if the cost of arranging the commitment is sufficiently small compared to the cost of cooperation, commitment arranging behavior is frequent, leading to a high level of cooperation in the population. Moreover, an optimal participation level emerges depending both on the dilemma at stake and on the cost of arranging the commitment. Namely, the harsher the common good dilemma is, and the costlier it becomes to arrange the commitment, the more participants should explicitly commit to the agreement to ensure the success of the joint venture. Furthermore, considering that commitment deals may last for more than one encounter, we show that commitment proposers can be lenient in case of short-term agreements, yet should be strict in case of long-term interactions.