We extend the convergence result of Hofbauer and Sorin for the best response differential inclusions coming from a nonconcave, nonconvex continuous payoff function U(x,y). A counterexample shows that convergence to a Nash equilibrium may not be true if we attempt to generalize the result to a three-person nonzero sum game.
Barron, E. N., Goebel, R., & Jensen, R. R. (2010). Best response dynamics for continuous games. Proceedings of the American Mathematical Society, 138(03), 1069–1069. https://doi.org/10.1090/s0002-9939-09-10170-3