We …rst scrutinize two extensions of the nucleolus for NTU games by Kalai(1975) and Nakayama(1983) ; respectively. We see that some nice things disappear during the process of extension. To de…ne the -nucleolus, the -excess function is de…ned and is axiomatized. It is nice to see that the -nucleolus satis…es the coincidence property and preserves many nice properties of the nucleolus for TU gam...

Exponential runtimes of algorithms for values games with transferable utility like the Shapley value are one biggest obstacles in practical application otherwise axiomatically convincing solution concepts cooperative game theory. We investigate to what extent hierarchical structure a level improves compared an unstructured player set. Representatively, we examine levels value, nested and, as ne...

In this paper, we study the egalitarian solution for games with discrete side payment, where characteristic function is integer-valued and payoffs of players are integral vectors. The solution, introduced by Dutta Ray in 1989, a concept transferable utility cooperative form, which combines commitment egalitarianism promotion indivisual interests consistent manner. We first point out that nice p...

In a fuzzy cooperative game the players may choose to partially participate in a coalition. A fuzzy coalition consists of a group of participating players along with their participation level. The characteristic function of a fuzzy game specifies the worth of each such coalition. This paper introduces well-known properties of classical cooperative games to the theory of fuzzy games, and studies...

We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One o...

The Value is a solution concept originally due to Shapley (1953). The idea behind the concept is to evaluate how much will a player be willing to pay to participate in a given game. It seeks to represent what the game is worth for a player. In some sense the value captures the expected outcome of the game. We will start with the TU (transferable utility) framework and the axiomatic approach and...

Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...

We present sufficient conditions for monotone matching in environments where utility is not fully transferable between partners. These conditions involve not only complementarity in types of the total payoff to a match, as in the transferable utility case, but also monotonicity in type of the degree of transferability between partners. We apply our conditions to study some models of risk sharin...

We present sufficient conditions for monotone matching in environments where utility is not fully transferable between partners. These conditions involve complementarity in types not only of the total payoff to a match, as in the transferable utility case, but also in the degree of transferability between partners. We apply our conditions to study some models of risk sharing and incentive probl...