Converging to Team-Maxmin Equilibria in Zero-Sum Multiplayer Games

Jul 12, 2020

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Efficiently computing equilibria for multiplayer games is still an open challenge in computational game theory. This paper focuses on computing Team-Maxmin Equilibria (TMEs), which is an important solution concept for zero-sum multiplayer games where players in a team having the same utility function play against an adversary independently. Existing algorithms are inefficient to compute TMEs in large games, especially when the strategy space is too large to be represented due to limited memory. In two-player games, the Incremental Strategy Generation (ISG) algorithm is an efficient approach to avoid enumerating all pure strategies. However, the study of ISG for computing TMEs is completely unexplored. To fill this gap, we first study the properties of ISG for multiplayer games, showing that ISG converges to a Nash equilibrium (NE) but may not converge to a TME. Second, we design an ISG variant for TMEs (ISGT) by exploiting that a TME is an NE maximizing the team’s utility and show that ISGT converges to a TME and the impossibility of relaxing conditions in ISGT. Third, to further improve the scalability, we design an ISGT variant (CISGT) by using the strategy space for computing an equilibrium that is close to TME but is easier to be computed as the initial strategy space of ISGT. Finally, extensive experimental results show that CISGT is orders of magnitude faster than ISGT and the state-of-the-art algorithm to compute TMEs in large games.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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