  We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in
dynamic games, extending the Feedback Nash Equilibrium concept to games in
which players are subject to state and input constraints. We formalize
necessary and sufficient conditions for (local) GFNE solutions at the
trajectory level, which enable the development of efficient numerical methods
for their computation. Specifically, we propose a Newton-style method for
finding game trajectories which satisfy necessary conditions for an
equilibrium, which can then be checked against sufficiency conditions. We show
that the evaluation of the necessary conditions in general requires computing a
series of nested, implicitly-defined derivatives, which quickly becomes
intractable. To this end, we introduce an approximation to the necessary
conditions which is amenable to efficient evaluation, and in turn, computation
of solutions. We term the solutions to the approximate necessary conditions
Generalized Feedback Quasi-Nash Equilibria (GFQNE), and we introduce numerical
methods for their computation. In particular, we develop a Sequential
Linear-Quadratic Game approach, in which a LQ local approximation of the game
is solved at each iteration. The development of this method relies on the
ability to compute a GFNE to inequality- and equality-constrained LQ games, and
therefore specific methods for the solution of these special cases are
developed in detail. We demonstrate the effectiveness of the proposed solution
approach on a dynamic game arising in an autonomous driving application.
