On skew-symmetric games

Hao, Yaqi; Cheng, Daizhan

doi:10.1016/j.jfranklin.2018.02.015

Cited by 27 publications

(12 citation statements)

References 20 publications

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“…Remark 2 In [15] and [20], construction algorithms of a group of bases for the symmetric game subspace are given by using the classification of strategy profiles. Different from [15] and [20], Theorem 4 directly constructs a group of bases of a symmetric game subspace from a group of bases of the solution space of linear equations (43). In addition, the testing equations for symmetric games with the minimum number is easily obtained.…”

Section: Symmetric Games and Testing Conditionsmentioning

confidence: 99%

“…Furthermore, for Boolean games, a group of bases of the symmetric game subspace is constructed via a recursive procedure in [9]. For general finite games, construction algorithms of bases of symmetric game subspaces are given in [15] and [20], respectively. It should be noted that the concept of strategy multiplicity vector and an equivalent condition for symmetric games in [4] play an important role in [9] [15] and [20].…”

Section: Introductionmentioning

confidence: 99%

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On Matrix Method of Symmetric Games

Wang¹,

Liu²,

Li³

et al. 2022

Preprint

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This paper provides a new version of matrix semi-tensor product method based on adjacent transpositions to test symmetric games. The advantage of using adjacent transpositions lies in the great simplification of analysis of symmetric games. By using the new method, new necessary and sufficient conditions for symmetric games are proposed, and a group of bases of a symmetric game space can be easily calculated. Moreover, the testing equations with the minimum number can be concretely determined. Finally, two examples are displayed to show the effectiveness of the proposed method.

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Section: Symmetric Games and Testing Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Matrix Method of Symmetric Games

Wang¹,

Liu²,

Li³

et al. 2022

Preprint

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“…As an opponent type of games, antisymmetric games are considered in [28]. Then based on symmetry and antisymmetry, another orthogonal decomposition was discussed.…”

Section: F Symmetric/antisymmetric Gamesmentioning

confidence: 99%

A Comprehensive Survey on STP Approach to Finite Games

Cheng¹,

Wu²,

Zhao³

et al. 2021

Preprint

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Nowadays the semi-tensor product (STP) approach to finite games has become a promising new direction. This paper provides a comprehensive survey on this prosperous field. After a brief introduction for STP and finite (networked) games, a description for the principle and fundamental technique of STP approach to finite games is presented. Then 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.

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“…Note that such decomposition is not unique. Recently, based on symmetric games and skew symmetric games another orthogonal decomposition is proposed as in (65), where S, K and E are subspaces of symmetric games, skew symmetric games and asymmetric games respectively [75].…”

Section: Identification Of Logical Systemsmentioning

confidence: 99%

From STP to game-based control

Cheng

Liu

2017

Sci. China Inf. Sci.

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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.

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On skew-symmetric games

Cited by 27 publications

References 20 publications

On Matrix Method of Symmetric Games

On Matrix Method of Symmetric Games

A Comprehensive Survey on STP Approach to Finite Games

From STP to game-based control

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