Acceptability-driven adaptive migration promotes cooperation in human–machine hybrid population

Sustaining cooperation in social systems is persistently challenged by the destabilizing influence of selfish behavior. In human–machine hybrid networks, interactions between artificial agents and human participants introduce both new obstacles and new opportunities for maintaining sustained cooperation. Social interactions are strongly influenced by individuals’ affective assessments of peer strategies. Here, “acceptability”—the degree to which an individual’s strategy is supported by neighbors—drives emotion-based migration toward more favorable positions. By contrast, cooperative robots are unaffected by such emotional evaluations and instead base their migration decisions on either success-driven movement or random exploration. Inspired by this notion, the Acceptability-Driven Adaptive Migration (ADAM) model is proposed. Monte Carlo (MC) simulations demonstrate that the proposed ADAM model effectively fosters the emergence of cooperative strategies. In populations where ordinary nodes migrate according to acceptability, increasing the proportion of cooperative robots markedly enhances cooperation, while node density exerts minimal influence except at extremely high or low levels. When a greater share of robots follow the success-driven rule rather than random exploration, cooperation is further reinforced. Network-level average acceptability improves when robots constitute either a minority or a majority of the population.