Research On Big Boss Interval Game With Interval Payoffs Theory And Application

In classical cooperative game theory, the payoffs of the coalitions are all exact values.However, due to practical problems is more complex, uncertain, so in order to more close toreality, scholars put forward fuzzy cooperative game. This paper mainly introduces aspecial kind of cooperation game model-big boss games, and according to some maturetheory of classical big boss games, it will expand payoffs to the interval, thus providing atheoretical basis for this kind of games of payoffs.Firstly, this paper introduces the basic theory of classical cooperative game, includingthe classical cooperative model and two kinds of commonly used solutions, namely coreand Shapley value. Then introducing cooperative games with interval value payoffs, itraises the convex interval cooperative game, size monotone interval cooperative game andoperation and distribution of interval cooperative games.Secondly, introducing three properties which classical big boss game must satisfy, thispart does not only prove the equivalence conditions of core, but also give an application onthe economy of the model.Thirdly, according to the specific situation of reality that income or expenses can notdetermine, this part extends the classical big boss games to interval, and gives the model ofinterval big boss games, proving properties of its core. Studying the interval point and jointinterval of interval big boss games, prove its relationship with interval core; It alsoresearches the value and interval Shapley value of interval big boss games,and according to the distribution of the interval Shapley value, proves the relationshipbetween benefits of big boss and big coalition. Study the relationship between convexinterval game,concave interval game, boundary interval game and bigboss interval game, mainly proving on the basis of size monotone interval big boss game,the equivalence relation between convex interval game and interval benefits,and the equivalence relation between interval Shapley value,interval valueand convex interval game.Finally, application of four economic models of big boss interval games areintroduced， and the relations between various interval games and big boss intervalgames are applied to the models,researching each of them interval core,interval Shapleyvalue,interval value and providing a good theoretical basis for distribution of benefits in practical problems.