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Upon starting a collective endeavour, it is important to understand your partners’ preferences and howstrongly they commit to a common goal. Establishing a prior commitment or agreement in terms of pos-terior benefits and consequences from those engaging in it provides an important mechanism for securingcooperation. Resorting to methods from Evolutionary Game Theory (EGT), here we analyse how priorcommitments can also be adopted as a tool for enhancing coordination when its outcomes exhibit anasymmetric payoff structure, in both pairwise and multiparty interactions. Arguably, coordination is morecomplex to achieve than cooperation since there might be several desirable collective outcomes in a coor-dination problem (compared to mutual cooperation, the only desirable collective outcome in cooperationdilemmas). Our analysis, both analytically and via numerical simulations, shows that whether prior com-mitment would be a viable evolutionary mechanism for enhancing coordination and the overall populationsocial welfare strongly depends on the collective benefit and severity of competition, and more importantly,how asymmetric benefits are resolved in a commitment deal. Moreover, in multiparty interactions, priorcommitments prove to be crucial when a high level of group diversity is required for optimal coordination.The results are robust for different selection intensities. Overall, our analysis provides new insights intothe complexity and beauty of behavioral evolution driven by humans’ capacity for commitment, as wellas for the design of self-organised and distributed multi-agent systems for ensuring coordination amongautonomous agents.