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A survey of decision making in adversarial games

Science China(Information Sciences) 2024年第4期67卷 85-112页

作者： Xiuxian LI Min MENG Yiguang HONG Jie CHEN College of Electronics and Information Engineering Tongji University Shanghai Research Institute for Intelligent Autonomous Systems

In many practical applications, such as poker, chess, drug interdiction, cybersecurity, and national defense, players often have adversarial stances, i.e., the selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Therefore, adversarial games are important in realworld applications. However, only special adversarial games, such as Bayesian games, are reviewed in the literature. In this respect, this study aims to provide a systematic survey of three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, stackelberg(security) games, and zero-sum differential games, from an array of perspectives, including basic knowledge of game models,(approximate) equilibrium concepts, problem classifications, research frontiers,(approximate) optimal strategy-seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

关键词： adversarial games zero-sum games stackelberg games differential games Nash equilibrium correlated equilibrium regret

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Robust SOF stackelberg game for stochastic LPV systems

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Science China(Information Sciences) 2021年第10期64卷 21-38页

作者： Hiroaki MUKAIDANI Hua XU Graduate School of Advanced Science and Engineering Hiroshima University Faculty of Business Sciences The University of Tsukuba

A robust static output feedback（SOF） stackelberg game with multiple followers in stochastic linear parameter varying（LPV） systems is investigated. The conditions for the existence of a robust SOF stackelberg strategy set under H;constraints are established by the cross-coupled matrix inequality（CCMI）.To determine this strategy set, the optimization problems corresponding to the relevant cost bounds are defined, and their solution sets are derived using the Karush-Kuhn-Tucker conditions. The results show that the robust SOF stackelberg strategy set can be obtained by solving higher-order cross-coupled matrix equations（CCMEs）. Because CCMEs are complex and difficult to solve numerically, a heuristic algorithm is developed by combining the CCMEs with the CCMIs. The convergence property is proven using the Krasnoselskii-Mann（KM） iteration algorithm. Finally, two numerical examples are solved to demonstrate the reliability and usefulness of the proposed heuristic algorithm.

关键词： stackelberg games linear parameter varying (LPV) stochastic systems cross-coupled matrix equations (CCMEs)

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