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This paper studies stochastic games on large graphs and their graphon limits.We propose a new formulation of graphon games based on a single typicalplayer's label-state distribution. In contrast, other recently proposed modelsof graphon games work directly with a continuum of players, which involvesserious measure-theoretic technicalities. In fact, by viewing the label as acomponent of the state process, we show in our formulation that graphon gamesare a special case of mean field games, albeit with certain inevitabledegeneracies and discontinuities that make most existing results on mean fieldgames inapplicable. Nonetheless, we prove existence of Markovian graphonequilibria under fairly general assumptions, as well as uniqueness under amonotonicity condition. Most imporantly, we show how our notion of graphonequilibrium can be used to construct approximate equilibria for large finitegames set on any (weighted, directed) graph which converges in cut norm. Thelack of players' exchangeability necessitates a careful definition ofapproximate equilibrium, allowing heterogeneity among the players'approximation errors, and we show how various regularity properties of themodel inputs and underlying graphon lead naturally to different strengths ofapproximation.

A label-state formulation of stochastic graphon games and approximate equilibria on large networks