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This article examines mean-field-type game problems by means of a directmethod. We provide various solvable examples beyond the classicallinear-quadratic game problems. These include quadratic-quadratic games andgames with power, logarithmic, sine square, hyperbolic sine square payoffs.Non-linear state dynamics such as log-state, control-dependent regimeswitching, quadratic state, cotangent state and hyperbolic cotangent state areconsidered. We identify equilibrium strategies and equilibrium payoffs instate-and-conditional mean-field type feedback form. It is shown that a simpledirect method can be used to solve broader classes of non-quadraticmean-field-type games under jump-diffusion-regime switching Gauss-Volterraprocesses which include fractional Brownian motions and multi-fractionalBrownian motions. We provide semi-explicit solutions to the fully cooperative,noncooperative nonzero-sum, and adversarial game problems.

Semi-Explicit Solutions to some Non-Linear Non-Quadratic Mean-Field-Type Games: A Direct Method