Monotonic core solutions: Beyond Young's theorem

We introduce two new monotonicity properties for core concepts: single-valued solution concepts that always select a core allocation whenever the game is balanced (has a nonempty core). We present one result of impossibility for one of the properties and we pose several open questions for the second property. The open questions arise because the most important core concepts (the nucleolus and the per capita nucleolus) do not satisfy the property even in the class of convex games.TU games, monotonicity, nucleolus per capita, core

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

Implementing with veto players: a simple non cooperative game

The paper adapts a non cooperative game presented by Dagan, Serrano and Volij (1997) for bankruptcy problems to the context of TU veto balanced games. We investigate the relationship between the Nash outcomes of a noncooperative game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.

On monotonic core allocations for coalitional games whith veto players

We characterize a monotonic core concept defined on the class of veto balanced games. We also discuss what restricted versions of monotonicity are possible when selecting core allocations. We introduce a family of monotonic core concepts for veto balanced games and we show that, in general, the nucleolus per capita is not monotonic.monotonicity, core, nucleolus per capita, TU games

Egalitarian distributions in coalitional models: The Lorenz criterion

The paper presents a framework where the most important single-valued solutions in the literature of TU games are jointly analyzed. The paper also suggests that similar frameworks may be useful for other coalitional models.We are grateful for financial support provided by projects PB-96-1469-C-05-04 and BEC2000-0875 of the Spanish Ministry of Education and Science and project UPV00031.321-HA-7903/2000 of the University of The Basque Country

Monotonic core solutions: Beyond Young's theorem

We introduce two new monotonicity properties for core concepts: single-valued solution concepts that always select a core allocation whenever the game is balanced (has a nonempty core). We present one result of impossibility for one of the properties and we pose several open questions for the second property. The open questions arise because the most important core concepts (the nucleolus and the per capita nucleolus) do not satisfy the property even in the class of convex games.J. Arin acknowledges financial support from Project 9/UPV00031.321-15352/2003 of the University of the Basque Country, Projects BEC2003-08182 and SEJ-2006-05455 of the Ministry of Education and Science of Spain and Project GIC07/146-IT-377-07 of the Basque Goverment

Egalitarian distributions in coalitional models: The Lorenz criterion

The paper presents a framework where the most important single-valued solutions in the literature of TU games are jointly analyzed. The paper also suggests that similar frameworks may be useful for other coalitional models.coalitional games, egalitarian criteria, prenucleolus, Shapley value

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