The SD-prenucleolus for TU games

We introduce and characterize a new solution concept for TU games. The new soluction is called SD-prenucleolus and is a lexicographic value although is not a weighted prenucleolus. The SD-prenucleolus satisfies several desirable poperties and is the only known solution that satisfies core stability, strong aggegate monotonicity and null player out property in the class of balanced games. The SD-prenucleolus is the only known solution that satisfies core stability continuity and is monotonic in the class of veto balanced games.TU games, prenucleolus, per capita prenucleolus

The SD-prekernel for TU games

We introduce and analyze a new solution concept for TU games:The Surplus Distributor Prekernel. Like the prekermel, the new solu- tion is based on the an alternative motion of complaint of one player against other with respect to an allocation. The SD-prekernel contains the SD-prenucleolus and they coincide in the class of convex games. This result allows us to prove that in bankruptcy problems the SD-prekernel and the Minimal Overlapping rule select the same allocation.The Spanish Ministerio de Ciencia e Innovación under projects ECO2015-67519-P and ECO2009-11213, co-funded by the ERDF,and by Basque Government funding for Grupo Consolidado GIC07/146-IT-368-13

A monotonic core concept for convex games: The SD-prenucleolus

We prove that the SD-prenucleolus satisfies monotonicity in the class of convex games. The SD-prenucleolus is thus the only known continuous core concept that satisfies monotonicity for convex games. We also prove that for convex games the SD-prenucleolus and the SD-prekernel coincide.-Spanish Ministerio de Ciencia e Innovación under project ECO2012-31346.-Basque Government funding for Grupo Consolidado GIC07/146-IT-377-0

The coincidence of the kernel and nucleolus of a convex game: an alternative proof

In 1972, Maschler, Peleg and Shapley proved that in the class of convex the nucleolus and the kernel coincide. The only aim of this note is to provide a shorter, alternative proof of this result.Spanish Ministerio de Ciencia e Innovación under projects SEJ2006-05455 AND ECO2009-11213, co-funded by ERDF, and by Basque Government funding for Grupo Consolidado GIC07/146-IT-377-07

The SD-prenucleolus for TU games

We introduce and characterize a new solution concept for TU games. The new soluction is called SD-prenucleolus and is a lexicographic value although is not a weighted prenucleolus. The SD-prenucleolus satisfies several desirable poperties and is the only known solution that satisfies core stability, strong aggegate monotonicity and null player out property in the class of balanced games. The SD-prenucleolus is the only known solution that satisfies core stability continuity and is monotonic in the class of veto balanced games.J. Arin acknowledges the support of the Spanish Ministerio de Ciencia e Innovación under projects SEJ2006-05455 and ECO2009-11213, co-funded by ERDF, and by Basque Government funding for Grupo Consolidado GIC07/146-IT-377-07

On 1-convexity and nucleolus of co-insurance games

The situation, in which an enormous risk is insured by a number of insurance companies, is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we show that a co-insurance game possesses several interesting properties that allow to study the nonemptiness and the structure of the core and to construct an efficient algorithm for computing the nucleolus

Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication. © 2010 The Author(s)

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

TU-game, Nucleolus, Game with permission structure, Peer group game, Information market game, Algorithm, Complexity, C71,