  We present multilinear and mixed-integer multilinear programs to find a Nash
equilibrium in multi-player noncooperative games. We compare the formulations
to common algorithms in Gambit, and conclude that a multilinear feasibility
program finds a Nash equilibrium faster than any of the methods we compare it
to, including the quantal response equilibrium method, which is recommended for
large games. Hence, the multilinear feasibility program is an alternative
method to find a Nash equilibrium in multi-player games, and outperforms many
common algorithms. The mixed-integer formulations are generalisations of known
mixed-integer programs for two-player games, however unlike two-player games,
these mixed-integer programs do not give better performance than existing
algorithms.
