Efficiently computing Nash Equilibria in Multi-Adversarial Team Games
Résumé
Adversarial Team Games (ATG), as introduced by von Stengel and Koller, model strategic situations where a team of agents, sharing a common objective but unable to coordinate their actions, faces a single adversary. Recent advances have shown that computing an approximate Nash Equilibrium (NE) in ATGs is computationally tractable, establishing ATGs as one of the rare multi-agent game families where this holds. However, this tractability result is limited to single-adversary scenarios, leaving the common case of multiple independent adversaries — prevalent in applications such as anti-poaching, robotic planning, and hider-seeker games — largely unexplored. This paper addresses this gap by introducing the Multi-Adversarial Team Game (MATG) framework, a natural extension of ATGs to settings with multiple independent adversaries. Our main contribution is to prove that approximate NE computation remains tractable in this generalised setting. We achieve this by designing and analyzing a pseudo fully-polynomial time approximation scheme (pseudo-FPTAS) for computing NE in MATGs. Beyond our theoretical contributions, we provide the first implementation of this family of algorithms for NE computation in both ATGs and MATGs, demonstrating their empirical performance on a set of benchmark problems.
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