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We study continuous stochastic games with inhomogeneous mean fieldinteractions on large networks and explore their graphon limits. We consider amodel with a continuum of players, where each player's dynamics involve notonly mean field interactions but also individual jumps induced by a Poissonrandom measure. We examine the case of controlled dynamics, with control termspresent in the drift, diffusion, and jump components.  We introduce the graphon game model based on a graphon controlled stochasticdifferential equation (SDE) system with jumps, which can be regarded as thelimiting case of a finite game's dynamic system as the number of players goesto infinity. Under some general assumptions, we establish the existence anduniqueness of Markovian graphon equilibria. We then provide convergence resultson the state trajectories and their laws, transitioning from finite gamesystems to graphon systems. We also study approximate equilibria for finitegames on large networks, using the graphon equilibrium as a benchmark. Therates of convergence are analyzed under various underlying graphon models andregularity assumptions.

Stochastic Graphon Mean Field Games with Jumps and Approximate Nash Equilibria