Designing efficient algorithms to compute Nash equilibria poses considerable challenges in Algorithmic Game Theory and Optimization. In this work, we employ integer programming techniques to compute Nash equilibria in Integer Programming Games, a class of simultaneous and non-cooperative games where each player solves a parametrized integer program. We introduce ZERO Regrets, a general and efficient cutting plane algorithm to compute, enumerate, and select Nash equilibria. Our framework leverages the concept of equilibrium inequality, an inequality valid for any Nash equilibrium, and the associated equilibrium separation oracle. We evaluate our algorithmic framework on a wide range of practical and methodological problems from the literature, providing a solid benchmark against the existing approaches.

翻译：设计计算纳什平衡的高效算法在算法游戏理论和优化中提出了相当大的挑战。在这项工作中,我们使用整数编程技术在整数编程游戏中计算纳什平衡,这是一组同时和非合作的游戏,每个玩家在其中解决一个准美化整数程序。我们引入了ZERO Riscort,一种通用的高效切除飞机算法,用于计算、罗列和选择纳什平衡。我们的框架利用平衡不平等的概念,一种对任何纳什均衡都有效的不平等,以及相关的平衡分离。我们评估了我们从文献中得出的一系列广泛的实际和方法问题,为现有方法提供了坚实的基准。