Allocation Rules Based On Position Value And Its Application

Axiomatic method is the most basic method of cooperative game.Shapley value and its axiomatic characterization have a principal role in the classic cooperative game.Shapley value regards any set of participants as a feasible alliance.However,due to various restrictions among participants,it is not uncommon that the alliance cannot be completely formed.To solve the problem,Myerson proposed Graph game in 1977,which has laid a foundation for other types of restricted game.In 1988,Meessen considered the contributions of the links in the alliances and proposed an important allocation rule,called the Position value.We aim to study the allocation rule and its application based on position value.In graph games,we considers the reasonable allocation under the condition that the component efficiency is not applicable.By considering the cooperation ability in cooper-ation,we propose the efficient extension of Position value for graph games based on the strong degree.And we prove it is the unique solution that satisfies efficiency,distribu-tion of the surplus by strong degree,and coherence with the Position-value for connected graphs.By introducing the idea of two-step component-wise egalitarian,we propose the efficient two-step egalitarian surplus Position value,and it is the unique solution which satisfies the efficiency,fair distribution of surplus between components,fair distribution of surplus within component,and coherence with the Position-value for connected graph-s.We give the efficient egalitarian Position value by considering the egalitarian of each participant in the union.We provide its axiomatic characterizations combined with the efficient,fair distribution of surplus in union,and coherence with the Position-value for connected graphs.In addition,we gives the deletion link property of the efficient so-lutions.We provide relevant axiomatic characterizations combined with the efficient,corresponding deletion link property,and coherence with the Position-value for connect-ed graphs to these efficient solutions.Moreover,the three efficient solutions are analyzed with a case.In hypergraph games,we study the additive decomposition of the Position value.By considering each conference in hypergraphs not only affects the benefit of the players in the alliances associated with it,but also affects the benefit of the players in the alliances that are not associated with it,we introduce the within groups Position value and the between groups Position value on hypergraph games to distinguish the components of each player’s benefit.We give axiomatic characterizations for these two kinds of values Futhermore,we give an example to illustrate the within groups Position value and the between groups Position value.And we propose an improved allocation rule by adjusting the proportion of the intermediary cost.