In this paper we prove the existence and uniqueness of a solution concept for n-person games with fuzzy coalitions, which we call the Shapley mapping. The Shapley mapping, when it exists, associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a “cumulative value” that is the “su...

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core—the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external paym...

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core—the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external paym...

k-Anonymity is one of the most popular conventional techniques for protecting the privacy of an individual. The shortcomings in the process of achieving k-Anonymity are presented and addressed by using Coalitional Game Theory (CGT) [1] and Concept Hierarchy Tree (CHT). The existing system considers information loss as a control parameter and provides anonymity level (k) as output. This paper pr...

The Shapley value [46] is one of the most important solution concepts in coalitional game theory. It was originally defined for classical model of a coalitional game, which is relevant to a wide range of economic and social situations. However, while in certain cases the simplicity is the strength of the classical coalitional game model, it often becomes a limitation. To address this problem, a...

In this paper we propose two novel coalitional game theory based optimization methods for minimizing the cost of electricity consumed by households from a smart community. Some households in the community may own renewable energy systems (RESs) conjoined with energy storing systems (ESSs). Some other residences own ESSs only, while the remaining households are simple energy consumers. We first ...

We consider Effort Games, a game-theoretic model of cooperation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; carrying out certain subsets of the tasks completes the project successfully, while carrying out other subsets does not. The probability of carrying out a task is higher ...

In non-cooperative games, if coordination is allowed, then coalitions can take group actions, and thus become players themselves, each opposed to its complement. There is conflict when for every outcome there is at least one player who strictly prefers another outcome. In this paper, an index measuring conflict is provided. It obtains through a general procedure for turning any non-cooperative ...

The relationship between coalition-proof equilibria in a normal-form game and those in its subgame is examined. A subgame of a normal-form game is a game in which the strategy sets of all players in the subgame are subsets of those in the normal-form game. Ray (2001) proved that a Nash equilibrium of a subgame is a Nash equilibrium of the original game under the condition of no unilateral benef...

We consider the class of proper monotonic simple games and study coalition formation when an exogenous share vector and a solution concept are combined to guide the distribution of coalitional worth. Using a multiplicative composite solution, we induce players’ preferences over coalitions in a hedonic game, and present conditions under which the semistrict core of the game is nonempty. JEL Clas...