Rosenblatt processes are non-Gaussian, non-Poisson, and non-Markov with long-range dependence. This chapter examines a class of mean-field-type games driven by Rosenblatt processes. We provide expressions for equilibrium strategies and corresponding equilibrium costs in linear state-and-mean-field-type feedback form for all decision-makers. The cost functional is non-quadratic and includes a fractional integral of high-order polynomial. We show that the Ito’s formula for state dynamics of mean-field-type-driven Rosenblatt process involves the third (or higher) derivative of the cost function in the general setting.