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(netw...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.展开更多
This work studies the orthogonal decomposition of the incomplete-profile normal finite game(IPNFG)space using the method of semi-tensor product(STP)of matrices.Firstly,by calculating the rank of the incomplete-profile...This work studies the orthogonal decomposition of the incomplete-profile normal finite game(IPNFG)space using the method of semi-tensor product(STP)of matrices.Firstly,by calculating the rank of the incomplete-profile potential matrix,the bases of incomplete-profile potential game subspace(GPΩ)and incomplete-profile non-strategic game subspace(NΩ)are obtained.Then the bases of incomplete-profile pure potential game subspace(PΩ)and incomplete-profile pure harmonic game subspace(HΩ)are also revealed.These bases offer an expression for the orthogonal decomposition.Finally,an example is provided to verify the theoretical results.展开更多
The game theory was firstly used for description of economic phenomena and social interaction. But there are certain type of perfect information games （PI-games）, the so-called positional game or Banach-Mazur games,...The game theory was firstly used for description of economic phenomena and social interaction. But there are certain type of perfect information games （PI-games）, the so-called positional game or Banach-Mazur games, which so far have not been applied in economy. The perfect information positional game is defined as the game during which at any time the choice is made by one of the players who is acquainted with the previous decision of his opponent. The game is run on a sequential basis. The aim of this paper is to discuss selected Banach-Mazur games and to present some applications of positional game. This paper also shows new theoretical example of a determined PI-game, based by theoretical overview. All considerations are pure theoretical and based by logical deduction.展开更多
This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games(FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, ...This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games(FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, based on which, a more concise basis is constructed for the pure harmonic subspace. Second, based on the new basis of FPHGs and auxiliary harmonic vector, a more easily verifiable criterion is presented for the existence of pure Nash equilibrium in basis FPHGs. Third,by constructing a pure Nash equilibrium cubic matrix, the verification of pure Nash equilibrium in three-player FPHGs is given.展开更多
基金the National Natural Science Foundation of China(NSFC)under Grant Nos.62073315,61074114,and 61273013。
文摘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.
基金the Natural Science Foundation of Hebei Province under Grant Nos.F2021202032,A2019202205the Cultivation of Postgraduate Students Innovation Ability of Hebei Province under Grant No.CXZZSS2021045。
文摘This work studies the orthogonal decomposition of the incomplete-profile normal finite game(IPNFG)space using the method of semi-tensor product(STP)of matrices.Firstly,by calculating the rank of the incomplete-profile potential matrix,the bases of incomplete-profile potential game subspace(GPΩ)and incomplete-profile non-strategic game subspace(NΩ)are obtained.Then the bases of incomplete-profile pure potential game subspace(PΩ)and incomplete-profile pure harmonic game subspace(HΩ)are also revealed.These bases offer an expression for the orthogonal decomposition.Finally,an example is provided to verify the theoretical results.
文摘The game theory was firstly used for description of economic phenomena and social interaction. But there are certain type of perfect information games （PI-games）, the so-called positional game or Banach-Mazur games, which so far have not been applied in economy. The perfect information positional game is defined as the game during which at any time the choice is made by one of the players who is acquainted with the previous decision of his opponent. The game is run on a sequential basis. The aim of this paper is to discuss selected Banach-Mazur games and to present some applications of positional game. This paper also shows new theoretical example of a determined PI-game, based by theoretical overview. All considerations are pure theoretical and based by logical deduction.
基金supported by the National Natural Science Foundation of China under Grant No.62073202the Young Experts of Taishan Scholar Project under Grant No.tsqn201909076。
文摘This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games(FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, based on which, a more concise basis is constructed for the pure harmonic subspace. Second, based on the new basis of FPHGs and auxiliary harmonic vector, a more easily verifiable criterion is presented for the existence of pure Nash equilibrium in basis FPHGs. Third,by constructing a pure Nash equilibrium cubic matrix, the verification of pure Nash equilibrium in three-player FPHGs is given.
