We introduce the Cut-and-Play, an efficient algorithm for computing equilibria in simultaneous non-cooperative games where players solve nonconvex and possibly unbounded optimization problems. 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 original game and refines them with techniques from integer programming, for instance, cutting planes and branching operations. We test our algorithm on two families of challenging nonconvex games involving discrete decisions and bilevel programs, and we empirically demonstrate that it efficiently computes equilibria and outperforms existing game-specific algorithms.

翻译：我们提出切割-玩法算法（Cut-and-Play），一种用于计算同时非合作博弈中均衡的高效算法，其中玩家解决非凸且可能无界的优化问题。该算法利用了原始非凸博弈的均衡与其凸化对应博弈之间的内在关系。在实践中，切割-玩法算法构建了原始博弈的一系列凸逼近，并通过整数规划技术（例如，切割平面和分支操作）对其进行细化。我们在两类具有挑战性的非凸博弈（涉及离散决策和双层规划）上测试了该算法，并通过实验证明，它能高效计算均衡，且优于现有的特定博弈算法。