United We Fall: On the Nash Equilibria of Multiplex and Multilayer Network Games
Published in arXiv preprint arXiv:2402.06108, 2024
Recommended citation: Ebrahimi, R. and Naghizadeh, P., (2024). United We Fall: On the Nash Equilibria of Multiplex and Multilayer Network Games. arXiv preprint arXiv:2402.06108.. 1(1). https://arxiv.org/abs/2402.06108
We explore how the properties of the constituent networks of a multiplex or multilayer network can undermine or support the existence, uniqueness, and stability of the game’s Nash equilibria. Notably, we highlight that both the largest and smallest eigenvalues of the constituent networks (reflecting their connectivity and two-sidedness, respectively) are instrumental in determining the uniqueness of the multiplex or multilayer network game’s equilibrium. Together, our findings shed light on the reasons for the fragility of equilibria when agents interact over networks of networks, and point out potential interventions to alleviate them.
Recommended citation: Ebrahimi, R., & Naghizadeh, P. (2024). United We Fall: On the Nash Equilibria of Multiplex and Multilayer Network Games. arXiv preprint arXiv:2402.06108.