United We Fall: On the Nash Equilibria of Multiplex Network Games

We first show that in general, even if the constituent networks are guaranteed to have unique Nash equilibria in isolation, the resulting multiplex need not have a unique equilibrium. We then identify certain subclasses of networks wherein guarantees on the uniqueness of Nash equilibria on the isolated networks lead to the same guarantees on the multiplex network game. We further 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 network equilibrium.

Recommended citation: R. Ebrahimi and P. Naghizadeh. (2023). “United We Fall: On the Nash Equilibria of Multiplex Network Games”; 2023 59th Annual Allerton Conference on Communication, Control, and Computing (Allerton)