A Generic Multi-Player Transformation Algorithm for Solving Large-Scale Zero-Sum Extensive-Form Adversarial Team Games

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.Comment: 9 pages, 5 figures, NIPS 202

Computing Team-Maxmin Equilibria in Zero-Sum Multiplayer Extensive-Form Games

The study of finding the equilibrium for multiplayer games is challenging. This paper focuses on computing Team-Maxmin Equilibria (TMEs) in zero-sum multiplayer Extensive-Form Games (EFGs), which describes the optimal strategies for a team of players who share the same goal but they take actions independently against an adversary. TMEs can capture many realistic scenarios, including: 1) a team of players play against a target player in poker games; and 2) defense resources schedule and patrol independently in security games. However, the study of efficiently finding TMEs within any given accuracy in EFGs is almost completely unexplored. To fill this gap, we first study the inefficiency caused by computing the equilibrium where team players correlate their strategies and then transforming it into the mixed strategy profile of the team and show that this inefficiency can be arbitrarily large. Second, to efficiently solve the non-convex program for finding TMEs directly, we develop the Associated Recursive Asynchronous Multiparametric Disaggregation Technique (ARAMDT) to approximate multilinear terms in the program with two novel techniques: 1) an asynchronous precision method to reduce the number of constraints and variables for approximation by using different precision levels to approximate these terms; and 2) an associated constraint method to reduce the feasible solution space of the mixed-integer linear program resulting from ARAMDT by exploiting the relation between these terms. Third, we develop a novel iterative algorithm to efficiently compute TMEs within any given accuracy based on ARAMDT. Our algorithm is orders of magnitude faster than baselines in the experimental evaluation