Exploring cooperation evolution in biological and social systems through donation and moral sentiment

This study explores how donation mechanisms and moral sentiment influence the evolution of cooperation in biological and social systems. Using an evolutionary game theory framework, we model a spatial system where individuals can either cooperate or defect, examining how resource transfers from wealthier to poorer individuals shape cooperative dynamics. We introduce a moral sentiment parameter that grants cooperators intrinsic psychological benefits, offsetting the cost of donation and enhancing their overall fitness. Our findings reveal that moderate donation levels significantly stabilize cooperation, particularly in environments with strong incentives to defect. Moreover, moral sentiment bolsters cooperative strategies by making donation more sustainable. The interplay between donation and moral sentiment produces a nonlinear effect, where their combined influence promotes cooperation more effectively than either factor alone. Additionally, we analyze the spatial spread of cooperation, showing that moral sentiment plays a crucial role in maintaining and expanding cooperative behavior across a network. These insights contribute to a deeper understanding of how social and moral factors shape cooperation, with implications for both natural and human communities.