Prior literature shows that some mechanisms, e.g., commitment, could give rise to cooperation. However, participants' diverse propensities to cooperate may limit such mechanisms' effectiveness. Thus, we bring individual differences in their propensities to cooperate into the reasoning of long-term social dynamics of cooperation through an agent-based modeling approach. Our results suggest that commitment may still guarantee cooperation when individuals have different propensities to cooperate but has weaker effects, and the setups of commitment are also important. Our study highlights the importance of integrating individual preferences in analyzing collective dynamics of a population consisting of individuals of heterogeneous characteristics, thus offering implications to facilitate cooperation in rich real-world scenarios.