Manipulate holistic cooperation of population game: optimal induction strategy for a few irrational agents in social networks

In social networks, cooperation dilemmas among agents persist as a significant challenge. Existing research often emphasizes mild interactions among rational agents for autonomous cooperation, but it tends to overlook the impact of irrational agents’ decisions, particularly under intentional inductions. This paper proposes an optimal induction strategy to enhance overall cooperation within the network, even when only one irrational agent is involved. We employ a continuous action iterative prisoner dilemma framework to model multi-agent games and utilize a tracker to minimize cooperation costs. A heuristic regulation algorithm is employed to generate optimal induction strategies, which may involve selecting a rational agent as a proxy for the irrational one. Through theoretical analysis using the Lyapunov direct method, we demonstrate the convergence of game dynamics despite the presence of irrational agents. Numerical results validate the effectiveness of our proposed strategy in promoting holistic cooperation. These findings highlight the vulnerability of social networks to external incentives and pave the way for further research into optimizing multi-agent cooperation dynamics.