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A Comprehensive Survey on STP Approach to finite games

Journal of Systems Science & Complexity 2021年第5期34卷 1666-1680页

作者： CHENG Daizhan WU Yuhu ZHAO Guodong FU Shihua Key Laboratory of Systems and Control Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100190China. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education Dalian University of TechnologyDalian 116081China School of Mathematics and Statistics Shandong Normal UniversityJinan 250014China. School of Mathematical Sciences Liaocheng UniversityLiaocheng 252000China

Nowadays the semi-tensor product(STP)approach to finite games has become a promising new *** paper provides a comprehensive survey on this prosperous *** a brief introduction for STP and finite(networked)games,a description for the principle and fundamental technique of STP approach to finite games is *** several problems and recent results about theory and applications of finite games via STP are presented.A brief comment about the potential use of STP to artificial intelligence is also proposed.

关键词： finite game game-theoretic control potential game semi-tensor product vector space structure of finite game

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From STP to game-based control

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Science China(Information Sciences) 2018年第1期61卷 9-27页

作者： Daizhan CHENG Hongsheng QI Zequn LIU Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences University of Chinese Academy of Sciences

This paper provides a comprehensive survey on semi-tensor product(STP) of matrices and its applications to different disciplines. First of all, the STP and its basic properties are introduced. Meanwhile, its inside physical meaning is explained. Second, its application to conventional dynamic systems is presented. As an example, the region of attraction of stable equilibriums is discussed. Third, its application to logical systems is presented. Particularly, the algebraic state space representation of logical systems and the important role it plays in analysis and control of logical systems are emphasized. Fourth, its application to finite games is discussed. The most interesting problems include potential game, evolutionary game, and game theoretic control. Finally, the mathematical essence of STP is briefly introduced.

关键词： semi-tensor product of matrices Boolean network logical(control) system finite game game theoretic control

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