Modeling Spatial Public Goods Games with Differentiated Strategies and Asymmetric Payoff Allocation

Social dilemmas often arise in multiplayer settings where individuals must balance personal interests against collective gains. The public goods game (PGG), a canonical model for studying such dilemmas, typically assumes homogeneous strategies and uniform payoff allocation, oversimplifying real-world cooperative behavior. This study introduces a spatial PGG model on lattice networks that incorporates differentiated strategies, where individuals adopt distinct strategies toward different neighbors, and asymmetric payoff allocation mechanisms. Players are categorized as pure cooperators, pure defectors, or mixed strategy players, and payoffs are distributed unevenly based on strategic differentiation. Through extensive simulations, we analyze how these features influence cooperation dynamics. Results show that differentiated strategies significantly lower the threshold for cooperation to emerge, particularly when combined with asymmetric investment. Even under low enhancement factors, such differentiation fosters earlier and more widespread cooperative behavior. Asymmetric payoff allocation amplifies this effect by incentivizing cooperation and accelerating the decline of defection. Mixed strategy players act as transitional agents, smoothing the shift from defection to stable cooperation through adaptive payoff responses. Further robustness checks from the perspectives of network size, network structure, and initial cooperation rate confirm the robustness of these dynamics, thereby highlighting the general applicability of the model. These findings offer valuable insights for designing more effective cooperation-promoting policies and incentive structures in complex social systems.