Research On The Stability Of Alliance Structure Based On Game Theory

This paper is devoted to study the stability of coalition structure in different approaches and determine the stable conditions of coalition structure under the given approach.For the game with coalition structures,we are committed to using different approaches to find conditions that the coalition structure can become stability.In a conflict-controlled system,it is a very common situation where players or agents are divided into different groups and each player makes a choice of behaviour for the benefit of their subgroup or coalition to which he belongs.The most important point in this problem is to formulate the principles of stable coalition structures.In general case,the stability of coalition structure means that no one in the game wants to deviate and change his "position" in the coalition.But there are always some other deviations from the principles,which will affect the stability of coalition structure and the existence of stable coalition structure.In this paper,the innovative point is we give a new definition of stability of coalition structures with constraints on players' deviations.Firstly,we examined that there doesn't always exist stable coalition structures with respect to the Shapley value and the ES-value in four-person games.Therefore,we relax the conditions of the set of stable coalition structures,in order to get much more stable coalition structures.Then,a new definition of stability of coalition structures is given.What's more,we also prove the relationship between these two definitions.Finally,two models with coalition structures are considered and we use examples to illustrate the existence of stable coalition structures.