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