The evolution of zero-determinant strategies in public goods game

How self-interested individuals spontaneously evolve cooperative behavior remains a central question across sociology, economics, and evolutionary biology. Since the discovery of zero-determinant (ZD) strategies, there has been growing interest in understanding how these strategies promote cooperation and their evolutionary characteristics. However, the evolutionary dynamics of ZD strategies in public goods games remain largely unexplored. In this study, we investigate the performance of ZD strategies when interacting with unconditional cooperators, focusing on both the early-stage payoff advantage and the time required to reach evolutionary steady states, as influenced by the extortion factor. Our results reveal that higher extortion factors can significantly promote cooperative behavior. Furthermore, in the context of multi-player, multi-strategy interactions, we find that while extortionate strategies can facilitate cooperation in small populations, they are highly vulnerable to invasion in large populations. Evolutionary dynamics in such settings overwhelmingly favor strategies that promote mutual cooperation rather than exploitation. These findings offer new insights into the limitations and potential of ZD strategies in more complex social dilemmas and highlight the critical role of population structure and strategic diversity in the emergence of cooperation.