A Label-State Formulation of Stochastic Graphon Games and Approximate Equilibria on Large Networks

This paper studies stochastic games on large graphs and their graphon limits. We propose a new formulation of based single typical player’s label-state distribution. In contrast, other recently proposed models work directly with continuum players, which involves serious measure-theoretic technicalities. fact, by viewing the label as component state process, we show in our that are special case mean field games, albeit certain inevitable degeneracies discontinuities make most existing results inapplicable. Nonetheless, prove existence Markovian equilibria under fairly general assumptions well uniqueness monotonicity condition. Most importantly, how notion equilibrium can be used to construct approximate for finite set any (weighted, directed) graph converges cut norm. The lack players’ exchangeability necessitates careful definition equilibrium, allowing heterogeneity among approximation errors, various regularity properties model inputs underlying lead naturally different strengths approximation. Funding: D. Lacker was partially supported Air Force Office Scientific Research [Grant FA9550-19-1-0291] National Science Foundation [Award DMS-2045328].