In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp ca...In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.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
In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n^2 averages of values of the characteristic function of the gam...In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n^2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done.展开更多
This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the coopera...This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~展开更多
基金supported by Natural Science Foundation Youth Project of China (No. 71201089)National Natural Science Foundation of China (Nos. 71071018 and 71271217)Natural Science Foundation Youth Project of Shandong Province,China(No. ZR2012GQ005)
文摘In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.
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, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n^2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done.
基金supported by the National Natural Science Foundation of China under Grant Nos.71201089, 71271217,and 71071018the Natural Science Foundation of Shandong Province,China,under Grant No. ZR2012GQ005
文摘This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~
