  We study continuous stochastic games with inhomogeneous mean field
interactions on large networks and explore their graphon limits. We consider a
model with a continuum of players, where each player's dynamics involve not
only mean field interactions but also individual jumps induced by a Poisson
random measure. We examine the case of controlled dynamics, with control terms
present in the drift, diffusion, and jump components.
  We introduce the graphon game model based on a graphon controlled stochastic
differential equation (SDE) system with jumps, which can be regarded as the
limiting case of a finite game's dynamic system as the number of players goes
to infinity. Under some general assumptions, we establish the existence and
uniqueness of Markovian graphon equilibria. We then provide convergence results
on the state trajectories and their laws, transitioning from finite game
systems to graphon systems. We also study approximate equilibria for finite
games on large networks, using the graphon equilibrium as a benchmark. The
rates of convergence are analyzed under various underlying graphon models and
regularity assumptions.
