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 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
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
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.
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.
