Mean-Field-Type Games with Jump and Regime Switching

In this article, we study mean-field-type games with jump-diffusion and regime switching in which the payoffs and the state dynamics depend not only on the state-action profile of the decision-makers but also on a measure of the state-action pair. The state dynamics is a measure-dependent process with jump-diffusion and regime switching. We derive novel equilibrium systems to be solved. Two solution approaches are presented: (i) dynamic programming principle and (ii) stochastic maximum principle. Relationship between dual function and adjoint processes are provided. It is shown that the extension to the risk-sensitive case generates a nonlinearity to the adjoint process and it involves three other processes associated with the diffusion, jump and regime switching, respectively.