Graphon Games with Multiple Equilibria: Analysis and Computation

A graphon game can be seen either as a limit of a sequence of network games when the number of players tends to infinity or as a stochastic model for sampling network games. Under suitable assumptions, we show that every convergent sequence of Nash equilibria of network games sampled from a graphon game converges to an equilibrium of the graphon game with probability 1, and every equilibrium of a graphon game is a limit of a sequence of $ϵ$-Nash equilibria of network games sampled from the graphon game with probability 1. Further, we provide methods for computing the equilibria of two broad classes of graphon games modeling commonly observed interaction structures: graphon games with (i) a low-rank graphon and a polynomial best-response function and (ii) a stochastic block model graphon and finite strategy sets.

Funding: This material is based upon work supported by the National Science Foundation under Award No. ECCS-2340289.