  Solution methods for generalized Nash equilibrium have been dominated by
variational inequalities and complementarity problems. Since these approaches
fundamentally rely on the sufficiency of first-order optimality conditions for
the players' decision problems, they only apply as heuristic methods when the
players are modeled by nonconvex optimization problems. In contrast, this work
approaches generalized Nash equilibrium using theory and methods for the global
optimization of nonconvex bilevel programs. Through this perspective, we draw
precise connections between generalized Nash equilibria, feasibility for
bilevel programming, the Nikaido-Isoda function, and classic arguments
involving Lagrangian duality and spatial price equilibrium. Significantly, this
is all in a general setting without the assumption of convexity. Along the way,
we introduce the idea of minimum disequilibrium as a solution concept that
reduces to traditional equilibrium when equilibrium exists. The connections
with bilevel programming and related semi-infinite programming permit us to
adapt global optimization methods for those classes of problems, such as
constraint generation or cutting plane methods, to the problem of finding a
minimum disequilibrium solution. We propose a specific algorithm and show that
this method can find a pure Nash equilibrium even when the players are modeled
by mixed-integer programs.
