Mean-Field-Type Games driven by Rosenblatt Processes

This paper examines a class of mean-field-type games with finite numbers of decision-makers with state dynamics driven by Rosenblatt processes. Rosen-blatt processes are non-Gaussian, non-Poisson, and non-Markov with long-range dependence. We provide equilibrium strategies and equilibrium costs in linear state-and-mean-field-type feedback form for all decision-makers. Interestingly, we show that the equilibrium strategies for state driven by Brownian, multi-fractional Brownian, Gauss-Volterra processes no longer provide equilibrium in presence of Rosenblatt processes.