Evolutionary dynamics of networked multi-person games: mixing opponent-aware and opponent-independent strategy decisions

How rational individuals make strategic decisions when confronted with the temptation of defection is consistently a longstanding conundrum. Particularly, in a heterogeneous environment incorporating multiple decision rules, little is known about the evolutionary dynamics of networked multi-person games. To address this issue, we propose an original theoretical framework to investigate the hybrid dynamics for mixed opponent-aware and opponent-independent strategy decisions. We equip each agent with an individualized decision-making function, by which decision-makers cannot only select the information type but can also process it individually. Under weak selection, we theoretically derive a condition under which one strategy wins over the other, and accordingly we demonstrate that such an analogous criterion also holds in a mutation-selection process. For a hybrid system of two decision-making functions, we specifically prove that this condition is robust against population structures. Beyond weak selection, however, we find that the co-evolutionary dynamics induced by strategy adoption and decision-rule imitation are sensitive to the change of population structures. Our work, thus, clearly elucidate how the diversity and heterogeneity of individual decision-making affect the fate of strategy evolution, which may offer some insights into the evolution of cooperation.