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This work studies the behaviors of two large-population teams competing in adiscrete environment. The team-level interactions are modeled as a zero-sumgame while the agent dynamics within each team is formulated as a collaborativemean-field team problem. Drawing inspiration from the mean-field literature, wefirst approximate the large-population team game with its infinite-populationlimit. Subsequently, we construct a fictitious centralized system and transformthe infinite-population game to an equivalent zero-sum game between twocoordinators. We study the optimal coordination strategies for each team via anovel reachability analysis and later translate them back to decentralizedstrategies that the original agents deploy. We prove that the strategies are$\epsilon$-optimal for the original finite-population team game, and we furthershow that the suboptimality diminishes when team size approaches infinity. Thetheoretical guarantees are verified by numerical examples.

Zero-Sum Games between Large-Population Teams: Reachability-based Analysis under Mean-Field Sharing