The Study On Solutions Of Some Incomplete Cooperative Games

A cooperative game with a communication structure,the so-called graph game,can well reflect hierarchical relationship between the players and the situation of their communication.A cooperative game with a priori unions includes information on possible previous relationships between the players which could influence the way in which these players cooperate.A cooperative game with fuzzy coalitions reflects the situations where players have the possibility to cooperate with different participation levels,varying from noncooperation to full cooperation,and where the obtained reward depends on the levels of participation.These games belong to the incomplete cooperation game.More and more scholars have paid their attention on them.In this thesis,the solutions of the above three kinds of incomplete games and their extensions are studied,and the main contributions are as follows:(1)We determine link's adjacent communication structure by the adjacent relationship between links in communication structure.Then,using Myerson value of the link's adjacent communication situation and the proportion of the marginal contribution of two vertices in their link,we define the position value with weight of marginal contribution.Furthermore,at some communication situations,the weighted position value is characterized by component efficiency and balanced link contributions.Besides,we define the weighted average tree solution on the graph game with a system of positive weights,and propose two axiomatic characterizations for the cycle-free graph games.At last,these solutions are used to analyze the problem of river's water resources allocation.(2)In the game with fuzzy communication structure,players in a coalition need to measure their profit using their participation levels and communication capacities at every moment because these attributes are fuzzy when the game is proposed.Using fuzzy graph-theoretic ideas,we define and characterize the average tree solution on the two fuzzy graph restricted games,which are determined by different behaviors of the players.Finally,an illustrative example is given.(3)In the game with fuzzy coalition,we introduce the concept of continuous balanced almost-convex cooperative fuzzy game,and prove its bargaining set coincides with its Aubin core,which extends a result by Getá et al.for classical cooperative games to cooperative fuzzy games.What's more,we deal with the relationship between core and bargaining set in cooperative fuzzy games with Choquet integral forms.We introduce the concept of bargaining set for cooperative fuzzy games with Choquet integral forms and prove that for a convex cooperative fuzzy game with Choquet integral forms,its bargaining set coincides with its core,which extends a well-known result by Maschler et al.for classical cooperative games to cooperative fuzzy games.(4)In the fuzzy game with coalitional structures,we introduce the fuzzy coalitional-value,and propose some properties and characterization of this allocation rule.The fuzzy coalition-value is the generalization of the crisp coalitional-value.(5)In the situations of the incomplete cooperative game,both a coalition structure and a communication structure exist simultaneously and each of them mutually depends on each other.By using a two-step approach and solutions of the graph game,including Myerson value,position value and average tree solution,we define and axiomatize two new allocation rules of this kind game.