Explosive transitions in coevolutionary dynamics of synchronization and cooperation

Coordinated behavior is a fundamental feature of social and biological systems. Despite numerous studies on the emergence and maintenance of cooperation within the snowdrift game, the adaptive costs of cooperation are rarely considered. Here we integrate the Kuramoto model into the snowdrift game, where each oscillator interacts with its neighbors as a game participant. Strategy not only determines whether an oscillator is a cooperator or defector, but also dictates whether it engage in interactions to synchronize with neighbors. Synchronization level characterizes the degree of coordination among players, which influences the cost of cooperation. Here we show explosive transitions in both cooperation and synchronization on random networks. We also provide an analytical treatment to ground the observed scenarios. Our model offers a more nuanced characterization of game dynamics in real-world systems and provides insights into the interplay between synchronization and cooperation. While the snowdrift game, a social dilemma where individuals choose between cooperation and self-interest, has been extensively studied, the adaptive costs of cooperation remain underexplored. Here, the authors integrate the Kuramoto model into the snowdrift game, utilizing the synchronization level to characterize the degree of coordination among players, revealing explosive transitions in cooperation and synchronization that offer a nuanced understanding of game dynamics.