Extension Research On Solutions Of A Kind Of Restricted Cooperative Games

In the practice of real life cooperation,quite frequently,there are restrictions on the alliance of players,which means that some coalitions can not form or some players are unable to play a role in the coalition.Games with permission structures are a kind of cooperative games with restricted alliance,which can be used to describe the situations in which there are hierarchical organizations among the players.In view of the uncertainties in the real world and the diversity of the cooperation methods,this thesis studies the solution of this kind of cooperative games extendedly from the following two aspects.First of all,combined with the theory of fuzzy cooperative games,games with permission structures in fuzzy environment are discussed.Secondly,combined with the theory of games with coalition with structures,several kinds of games with restricted coalition structures are discussed.For all kinds of cooperative games,the definition of solution is given,the existence of solution is discussed,the properties of solution are proved,and the application of solution in revenue allocation problem is illustrated by numerical examples.The main work of this thesis is as follows:(1)The Shapley value of cooperative games with permission structures in fuzzy environmentThe Shapley values of cooperative games with permission structures and fuzzy payoffs are discussed by combining cooperative games with the permission structures and cooperative games with fuzzy payoffs.For interval cooperative games with the permission structures,the restricted games of this kind of cooperative games are defined on the basis of considering the influence of the permission structure in the cooperations,the interval Shapley permission value is defined by the interval Shapley value of the restricted game,axiomatization conclusion is proved,and an example is given to illustrate the application of the solution in revenue allocation problem.For cooperative games with fuzzy permission structures and fuzzy payoffs,the restricted games of this kind of cooperative games are defined by using the autonomous operator and fuzzy Choquet integral,and then the fuzzy Shapley permission value is defined by using the fuzzy Shapley value of the restricted game,the properties of solution are proved,and an example is given to illustrate the application of solution in the practical problem.(2)The cores of cooperative games with fuzzy payoffsThe cores of cooperative games with fuzzy payoffs are discussed,the conditions for the non-emptiness of the core in classical cooperative game theory are extended to the cooperative games with fuzzy payoffs,and then the results are applied to games with permission structures.Firstly,the conditions for the the non-emptiness of the interval core(I-core)are obtained by extending the core non-empty conditions in classical cooperative game,such as balanced games,convex games,to interval cooperative games.Secondly,for games with fuzzy payoffs,a numerical example is given to illustrate that the F-balancedness is only necessary but not sufficient for non-emptiness of fuzzy core(F-core).Games with trapezoidal fuzzy number payoffs are detailed discussed,the properties of the F-core are discussed and some sufficient conditions for the non-emptiness of F-core are given,these conditions generalize the corresponding conclusions both in classical cooperative games and interval games.Finally,the conclusions of the previous two parts are applied to games with permission structures and fuzzy payoffs.(3)Cooperative games with permission structure restrictions within priori unionsCooperative games in which players participate in cooperation by forming priori unions and there are permission structures within priori unions are discussed.By using the two-stage distribution idea of Owen value and taking into account the restriction of cooperation by permission struvtures within the priori unions,we define the coalition interior restriction Owen value and prove that this value is the unique solution satisfying efficiency,inessential player property,coalition symmetry,structural monotonicity within priori unions,necessary player property and additivity.Combining the two-step Shapley value(TS value)and conjunctive Shapley permission value,we define the coalition interior restriction TS value and prove that this value is the unique solution satisfying efficiency,coalitional inessential player property,coalition symmetry,structural monotonicity within priori unions,coalitonal necessary player property and additivity.We compare this two solutions and point out that the coalition interior restriction TS value weaken the inessential player property and strengthen the necessary player property relative to the coalition interior restriction Owen value.We also provide numerical examples to illustrate the applications of this two solutions in practice.(4)Cooperative games with permission structure restrictions among priori unionsCooperative games in which players participate in cooperation by forming priori unions and there are permission structures among priori unions are discussed.In the case where the prior union in the permission structure can be replaced by its internal nonempty subset,coalition restriction Owen value is defined by using the distribution idea of Owen value.For the general case,coalition restriction TS value is defined by using the distribution idea of TS value.The properties of the two solutions are proved,and their applications are illustrated by numerical examples.