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Main Authors: Guan, Yue, Afshari, Mohammad, Tsiotras, Panagiotis
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2303.12243
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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