A New Solution Of Cooperative Games: Matching Value

There are many important solution concepts in classical cooperative games, whichhave been studied for more than half a century. For different solution concepts, theircharacters and suitable application fields may vary. However, the relations among thesesolutions have not been unified and discussed in detail. With the coming of information age,cooperative game model has more and more applicability, so a new solution concept withmore advantages, especially with the advantage of computation convenience, is urgentlyrequired.In this paper, we mainly have a discussion on the two important parts of classicalcooperative games: the coalition formation and the profit allocation problem, then aconnection between these two parts are built by a new defined solution concept calledmatching value. Firstly, based on the analysis of the existing two solutions core andShapley value, an evolution process of coalition formation is analyzed, a matching theory isdeveloped, a new solution called matching value is defined and its relative properties andadvantages are discussed. Secondly, the possibility of the coalition formation process isdeeply researched, a matching value is obtained under total coalition structure and thematching value is proved by three axioms. Finally, by concrete examples, the rationalityand validity of the matching value is verified.Matching theory in this paper is obtained combing the theory of coalition formationand the profit allocation problem in classical cooperative game, the relations between thesetwo parts are further analyzed, and a new solution concept is defined. All the above theoriesand conclusions show us that they can serve as a guideline and reference for thedevelopment of cooperative games either in theory and application.