  We propose a framework to compute approximate Nash equilibria in integer
programming games with nonlinear payoffs, i.e., simultaneous and
non-cooperative games where each player solves a parametrized mixed-integer
nonlinear program. We prove that using absolute approximations of the players'
objective functions and then computing its Nash equilibria is equivalent to
computing approximate Nash equilibria where the approximation factor is
doubled. In practice, we propose an algorithm to approximate the players'
objective functions via piecewise linear approximations. Our numerical
experiments on a cybersecurity investment game show the computational
effectiveness of our approach.
