This work studies the behaviors of two large-population teams competing in a discrete environment. The team-level interactions are modeled as a zero-sum game while the agent dynamics within each team is formulated as a collaborative mean-field team problem. Drawing inspiration from the mean-field literature, we first approximate the large-population team game with its infinite-population limit. Subsequently, we introduce two fictitious coordinators and transform the infinite-population game to an equivalent zero-sum game between the two coordinators. Via a novel reachability analysis, we study the optimal coordination strategies, which induce decentralized strategies under the original information structure. We establish the $\epsilon$-optimality of the resulting team strategies for the finite-population game, with the sub-optimality diminishing as the team size approaches infinity. The theoretical guarantees are verified by numerical examples.

Zero-Sum Games between Mean-Field Teams: Reachability-Based Analysis under Mean-Field Sharing

Main Track - Game Theory and Economic Paradigms

technical paper

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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

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Zero-Sum Games between Mean-Field Teams: Reachability-Based Analysis under Mean-Field Sharing

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