Solutions For Cooperative Games With Restricted Coalition Formation

Which coalitions can be formed and how the obtained profit is distributed among all players are the basic problems of cooperative games.The classical cooperative game model usually assumes that any coalition can be formed,and only discusses the distribution of the worth of the grand coalition among the various players.However,for allocation problems in which the coalition formation is restricted,the classical cooperative game model loses its applicability.This paper is devoted to studying the structures and properties of solutions for cooperative games with restricted coalition formation.On one hand,we establish new cooperative game models where the coalition formation depends on the characteristic functions or solutions of games,propose corresponding solutions,and describe the properties of solutions.On the other hand,based on different cooperation goals and roles of players in different decision-making environments,we propose new solutions for games with restricted coalition formation.The main research results are as follows:1.We propose the concepts of objection and counter-objection to the ordered coalition by a pair of players.By constructing an order restricted game,we define and axiomatize allowable values of cooperative games with restricted permutations.Meanwhile,several possible extensions of allowable values are given.2.We establish an endogenous levels structure formation procedure with respect to the Shapley value adapted to super-additive cooperative games,and prove the stability of the improved Shapley value by two concepts of levels core and strong Nash equilibrium.Furthermore,the idea of the procedure is applied to cooperative games with levels structure,and the improved Shapley value is defined and axiomatized.3.We establish weighted hypergraph communication situations for players may have different weights in different conferences,propose that players who do not contribute to the communication between conferences should pay a part of fees to the common players,and then introduce the concept of power measure.Moreover,the power surplus solution is defined and axiomatized,and two examples are provided to introduce the application of the solution.4.Based on the concept of level partition,we propose position values for communication situations with fuzzy coalitions by defining the link game.In addition,axiomatizations of position values are provided.5.We define and axiomatizes average tree values for communication situations by introducing the concept of cooperation relationship.Furthermore,the fuzzy version of average tree values is defined for communication situations with fuzzy coalitions.