Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no...Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.展开更多
In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given se...In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.展开更多
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
文摘Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.
基金the National Natural Science Foundation of China under Grants 61673012 and 11971240,respectively。
文摘In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.
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.
