Steering cooperation: Adversarial attacks on prisoner's dilemma in complex networks

TL;DR

The findings reveal that adversarial attacks on social networks can be potent tools for both promoting and inhibiting cooperation, opening new possibilities for controlling cooperative behavior in social systems while also highlighting potential risks.

Abstract

This study examines the application of adversarial attack concepts to control the evolution of cooperation in the prisoner's dilemma game in complex networks. Specifically, it proposes a simple adversarial attack method that drives players' strategies towards a target state by adding small perturbations to social networks. The proposed method is evaluated on both model and real-world networks. Numerical simulations demonstrate that the proposed method can effectively promote cooperation with significantly smaller perturbations compared to other techniques. Additionally, this study shows that adversarial attacks can also be useful in inhibiting cooperation (promoting defection). The findings reveal that adversarial attacks on social networks can be potent tools for both promoting and inhibiting cooperation, opening new possibilities for controlling cooperative behavior in social systems while also highlighting potential risks.

Figures (4)

• Figure 1: Line plots of the proportion of cooperators $\rho$ versus the advantage of defectors $b$ in (a) Erdős--Rényi (ER) random networks, (b) Barabási--Albert (BA) scale-free networks, and (c) Watts--Strogatz (WS) small-world networks, showing that adversarial attacks ($\epsilon$) can both promote ($\epsilon > 0$) and inhibit ($\epsilon < 0$) cooperation.
• Figure 2: Line plots of the proportion of cooperators $\rho$ versus perturbation strength $\epsilon$ for adversarial attacks promoting cooperation ($\epsilon > 0$) in (a) Erdős--Rényi (ER) random networks, (b) Barabási--Albert (BA) scale-free networks, and (c) Watts--Strogatz (WS) small-world networks, showing that adversarial attacks promote cooperation substantially more effectively than random attacks and Li et al.'s method The advantage of defectors $b$ is 1.35, 1.95, and 1.2 for (a), (b), and (c), respectively. These $b$ values are chosen as the maximum values for which $\rho \leq 0.1$ when $\epsilon = 0$ in Fig. \ref{['fig:rho_vs_b_wrt_eps_model']}, or set to 1.95 if no such value exists within $1 < b < 2$ (as in Fig. \ref{['fig:rho_vs_b_wrt_eps_model']}b).
• Figure 3: Line plots of the proportion of cooperators $\rho$ versus perturbation strength $|\epsilon|$ for adversarial attacks inhibiting cooperation ($\epsilon < 0$) in (a) Erdős--Rényi (ER) random networks, (b) Barabási--Albert (BA) scale-free networks, and (c) Watts--Strogatz (WS) small-world networks, showing that adversarial attacks inhibit cooperation substantially more effectively than random attacks and Li et al.'s method. The advantage of defectors over cooperators $b$ is 1.1, 1.5, and 1.05 for (a), (b), and (c), respectively. These $b$ values are chosen as the maximum values for which $\rho \geq 0.9$ when $\epsilon = 0$ in Fig. \ref{['fig:rho_vs_b_wrt_eps_model']}, or set to 1.05 if no such value exists within $1 < b < 2$ (as in Fig. \ref{['fig:rho_vs_b_wrt_eps_model']}c).
• Figure 4: Line plots of the proportion of cooperators $\rho$ versus the advantage of defectors over cooperators $b$ for different $\epsilon$ in (a) Facebook ($N=4039$ and $\langle k\rangle = 43.7$), (b) Advogato ($N=5054$ and $\langle k\rangle = 16.6$), (c) AnyBeat ($N=12645$ and $\langle k\rangle = 7.8$), and (d) HAMSTERster networks ($N=2000$ and $\langle k\rangle = 16.1$), showing that adversarial attacks ($\epsilon$) can both promote ($\epsilon > 0$) and inhibit ($\epsilon < 0$) cooperation.