Extendable Cooperative Games

Extendable cooperative games

A (TU) cooperative game is extendable (Kikuta and Shapley, 1986) if every core allocation of each sub-game can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its sub-games can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core (Sharkey, 1982). Further, we character...

A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

Cooperative Games

A coalitional (or cooperative) game is a model of interacting decision-makers that focuses on the behavior of groups of players. N denotes the set of players. A coalition is a group of players S ⊂ N . We refer to N as the grand coalition. Every coalition S has a set of available actions AS. An outcome consists of a partition of N (coalition structure) and one action associated with each coaliti...

Cooperative games

Cooperative Benefit and Cost Games under Fairness Concerns

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...