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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.12243 |
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| _version_ | 1866917595813249024 |
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| author | Guan, Yue Afshari, Mohammad Tsiotras, Panagiotis |
| author_facet | Guan, Yue Afshari, Mohammad Tsiotras, Panagiotis |
| contents | 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 construct a fictitious centralized system and transform the infinite-population game to an equivalent zero-sum game between two coordinators. We study the optimal coordination strategies for each team via a novel reachability analysis and later translate them back to decentralized strategies that the original agents deploy. We prove that the strategies are $ε$-optimal for the original finite-population team game, and we further show that the suboptimality diminishes when team size approaches infinity. The theoretical guarantees are verified by numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_12243 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Zero-Sum Games between Large-Population Teams: Reachability-based Analysis under Mean-Field Sharing Guan, Yue Afshari, Mohammad Tsiotras, Panagiotis Systems and Control 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 construct a fictitious centralized system and transform the infinite-population game to an equivalent zero-sum game between two coordinators. We study the optimal coordination strategies for each team via a novel reachability analysis and later translate them back to decentralized strategies that the original agents deploy. We prove that the strategies are $ε$-optimal for the original finite-population team game, and we further show that the suboptimality diminishes when team size approaches infinity. The theoretical guarantees are verified by numerical examples. |
| title | Zero-Sum Games between Large-Population Teams: Reachability-based Analysis under Mean-Field Sharing |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2303.12243 |