In this tutorial, we present a computational overview on computing Nash equilibria in Integer Programming Games ($IPG$s), $i.e.$, how to compute solutions for a class of non-cooperative and nonconvex games where each player solves a mixed-integer optimization problem. $IPG$s are a broad class of games extending the modeling power of mixed-integer optimization to multi-agent settings. This class of games includes, for instance, any finite game and any multi-agent extension of traditional combinatorial optimization problems. After providing some background motivation and context of applications, we systematically review and classify the state-of-the-art algorithms to compute Nash equilibria. We propose an essential taxonomy of the algorithmic ingredients needed to compute equilibria, and we describe the theoretical and practical challenges associated with equilibria computation. Finally, we quantitatively and qualitatively compare a sequential Stackelberg game with a simultaneous $IPG$ to highlight the different properties of their solutions.

翻译：在本教程中，我们针对整数规划博弈（$IPG$s）中的纳什均衡计算提供计算性概述，即如何求解一类每个参与者解决混合整数优化问题的非合作非凸博弈。$IPG$s是一类广泛博弈，将混合整数优化的建模能力扩展到多智能体场景。此类博弈包括任何有限博弈以及传统组合优化问题的多智能体扩展。在提供背景动机与应用场景后，我们系统回顾并分类了计算纳什均衡的最先进算法。我们提出一种必要的算法要素分类法以计算均衡，并描述了与均衡计算相关的理论与实践挑战。最后，我们通过定量与定性比较序列式斯塔克尔伯格博弈与同步$IPG$，突出其解的不同性质。