Mean Field Game with Reflected Jump Diffusion Dynamics: A Linear Programming Approach

Abstract: This paper develops a linear programming approach for mean field games with reflected jump-diffusion state dynamices. The jump component is driven by a Poisson process with time-varying intensity, and the multi-dimensional reflections enforce the state process to stay in a bounded domain. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak relaxed control formulation under some measurability conditions on model coefficients. Building upon the characterization of the occupation measure in the equivalence result, we further establish the existence of linear programming mean field equilibria under mild continuity conditions on model coefficients.