  We introduce Cut-and-Play, a practically-efficient algorithm for computing
Nash equilibria in simultaneous non-cooperative games where players decide via
nonconvex and possibly unbounded optimization problems with separable payoff
functions. Our algorithm exploits an intrinsic relationship between the
equilibria of the original nonconvex game and the ones of a convexified
counterpart. In practice, Cut-and-Play formulates a series of convex
approximations of the game and iteratively refines them with cutting planes and
branching operations. Our algorithm does not require convexity or continuity of
the player's optimization problems and can be integrated with existing
optimization software. We test Cut-and-Play on two families of challenging
nonconvex games involving discrete decisions and bilevel problems, and we
empirically demonstrate that it efficiently computes equilibria while
outperforming existing game-specific algorithms.
