Many recent practical and theoretical breakthroughs focus on adversarial team multi-player games (ATMGs) in ex ante correlation scenarios. In this setting, team members are allowed to coordinate their strategies only before the game starts. Although there existing algorithms for solving extensive-form ATMGs, the size of the game tree generated by the previous algorithms grows exponentially with the number of players. Therefore, how to deal with large-scale zero-sum extensive-form ATMGs problems close to the real world is still a significant challenge. In this paper, we propose a generic multi-player transformation algorithm, which can transform any multi-player game tree satisfying the definition of AMTGs into a 2-player game tree, such that finding a team-maxmin equilibrium with correlation (TMECor) in large-scale ATMGs can be transformed into solving NE in 2-player games. To achieve this goal, we first introduce a new structure named private information pre-branch, which consists of a temporary chance node and coordinator nodes and aims to make decisions for all potential private information on behalf of the team members. We also show theoretically that NE in the transformed 2-player game is equivalent TMECor in the original multi-player game. This work significantly reduces the growth of action space and nodes from exponential to constant level. This enables our work to outperform all the previous state-of-the-art algorithms in finding a TMECor, with 182.89, 168.47, 694.44, and 233.98 significant improvements in the different Kuhn Poker and Leduc Poker cases (21K3, 21K4, 21K6 and 21L33). In addition, this work first practically solves the ATMGs in a 5-player case which cannot be conducted by existing algorithms.

翻译：近期许多实践与理论突破聚焦于事前关联场景下的对抗团队多玩家博弈（ATMG），在该设定中，团队成员仅允许在游戏开始前协调策略。尽管已有求解扩展式ATMG的算法，但现有算法生成的博弈树规模随玩家数量呈指数增长。因此，如何求解接近现实世界的大规模零和扩展式ATMG问题仍是重大挑战。本文提出一种通用多玩家转化算法，可将任意满足ATMG定义的多玩家博弈树转化为双玩家博弈树，从而将大规模ATMG中寻找带关联性的团队最大最小均衡（TMECor）问题转化为求解双玩家博弈的纳什均衡。为实现该目标，我们首先引入名为"私有信息前分支"的新结构，该结构由临时机会节点与协调节点组成，旨在代表团队成员对所有潜在私有信息进行决策。我们还在理论上证明转化后双玩家博弈中的纳什均衡等价于原始多玩家博弈中的TMECor。本工作将动作空间与节点数的增长规模从指数级显著降低至常数级，使得我们在不同Kuhn扑克与Leduc扑克案例（21K3、21K4、21K6、21L33）中求解TMECor时，相较于所有先前最先进算法分别实现182.89、168.47、694.44及233.98倍的显著提升。此外，本工作首次实际求解了现有算法无法处理的五玩家ATMG案例。