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.