With respect to multichoice games with a coalition structure,a coalitional value named the generalized symmetric coalitional Banzhaf value is defined,which is an extension of the Shapley value for multichoice games an...With respect to multichoice games with a coalition structure,a coalitional value named the generalized symmetric coalitional Banzhaf value is defined,which is an extension of the Shapley value for multichoice games and the symmetric coalitional Banzhaf value for traditional games with a coalition structure.Two axiomatic systems are established:One is enlightened by the characterizations for the symmetric coalitional Banzhaf value,and the other is inspired by the characterizations for the Banzhaf value.展开更多
In this paper,we study a pursuit-evasion differential game problem in the Hilbert space L2.Dynamics of countable number of pursuers and evader expressed as nth-order differential equa-tions with geometric constraints ...In this paper,we study a pursuit-evasion differential game problem in the Hilbert space L2.Dynamics of countable number of pursuers and evader expressed as nth-order differential equa-tions with geometric constraints on the control functions of the players.The game terminates at a given fixed time which is denoted by 0.The game's payoff is the infimum of the distances between the evader and pursuers at the time 0.According to the rule of the game,pursuers try to minimise the distance to the evader and the evader tries to maximises it.We found value of the game and constructed players'optimal strategies.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71201089,71201110,71271217,and 71271029the Natural Science Foundation Youth Project of Shandong Province,China under Grant No.ZR2012GQ005+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20111101110036the Program for New Century Excellent Talents in University of China under Grant No.NCET-12-0541
文摘With respect to multichoice games with a coalition structure,a coalitional value named the generalized symmetric coalitional Banzhaf value is defined,which is an extension of the Shapley value for multichoice games and the symmetric coalitional Banzhaf value for traditional games with a coalition structure.Two axiomatic systems are established:One is enlightened by the characterizations for the symmetric coalitional Banzhaf value,and the other is inspired by the characterizations for the Banzhaf value.
文摘In this paper,we study a pursuit-evasion differential game problem in the Hilbert space L2.Dynamics of countable number of pursuers and evader expressed as nth-order differential equa-tions with geometric constraints on the control functions of the players.The game terminates at a given fixed time which is denoted by 0.The game's payoff is the infimum of the distances between the evader and pursuers at the time 0.According to the rule of the game,pursuers try to minimise the distance to the evader and the evader tries to maximises it.We found value of the game and constructed players'optimal strategies.
