Partially Observed Discrete-Time Risk-Sensitive Mean Field Games

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behavior for each agent via an exponential utility function. game model, is weakly coupled rest of population through its individual cost and state dynamics empirical distribution states. establish equilibrium in infinite-population limit using technique converting underlying original stochastic control problem to a fully one on belief space dynamic programming principle. Then, show that policy, when adopted by agent, forms approximate Nash sufficiently many agents. first finite-horizon function then discuss extension result infinite-horizon next-to-last section paper.