The Cut-and-Play Algorithm: Computing Nash Equilibria via Outer Approximations

• 成果类型: Article; Early Access
• 署名作者: Carvalho, Margarida; Dragotto, Gabriele; Lodi, Andrea; Sankaranarayanan, Sriram
• 署名单位: Universite de Montreal; Princeton University; Technion Israel Institute of Technology; Indian School of Business (ISB)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0327
• 发表日期: 2025
• 关键词: design; games; MODEL

摘要

We introduce Cut-and-Play, a practically efficient algorithm for computing Nash equilibria in simultaneous noncooperative 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.