Coalitionally monotonic set-solutions for cooperative TU games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the tradeoff between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core selection requirement by the core-extension property.

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

Regular population monotonic allocation schemes and the core

A subclass of games with population monotonic allocation schemes is studied, namelygames with regular population monotonic allocation schemes (rpmas). We focus on theproperties of these games and we prove the coincidence between the core and both theDavis-Maschler bargaining set and the Mas-Colell bargaining set

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

On the monotonic core

The monotonic core of a cooperative game with transferable utility (T.U.-game) is the set formed by all its Population Monotonic Allocation Schemes. In this paper we show that this set always coincides with the core of a certain game associated to the initial game.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Coalitionally monotonic set-solutions for cooperative TU games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the tradeoff between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core selection requirement by the core-extension property.

On the coincidence between the Shimomura's bargaining sets and the core

[cat] En l'article es dona una condició necessària per a que els conjunts de negociació definits per Shimomura (1997) i el nucli d'un joc cooperatiu amb utilitat transferible coincideixin. A tal efecte, s'introdueix el concepte de vectors de màxim pagament. La condició necessària consiteix a verificar que aquests vectors pertanyen al nucli del joc.

A security layer for JXTA core protocols

JXTA define un conjunto de seis protocolos básicos especialmente adecuados para una computación ad hoc, permanente, multi-hop, peer-to-peer (P2P). Estos protocolos permiten que los iguales cooperen y formen grupos autónomos de pares. Este artículo presenta un método que proporciona servicios de seguridad en los protocolos básicos: protección de datos, autenticidad, integridad y no repudio. Los mecanismos que se presentan son totalmente distribuidos y basados ¿¿en un modelo puro peer-to-peer, que no requieren el arbitraje de un tercero de confianza o una relación de confianza establecida previamente entre pares, que es uno de los principales retos en este tipo de entornos.

Assignment markets with the same core

[spa] En el contexto de los juegos de asignación bilaterales, estudiamos el conjunto de matrices asociadas a mercados de asignación con el mismo nucleo. Se proporcionan condiciones sobre las entradas de la matriz que aseguran que los juegos de asignación asociados tienen el mismo núcleo. Se prueba que este conjunto de matrices que dan lugar al mismo núcleo forman un semirretículo con un número finito de elementos minimales y un único máximo. Se da una caracterización de estos elementos minimales. También se proporciona una condición suficiente para obtener un retículo.

Multi-sided Böhm-Bawerk assignment markets: the core

[cat] En aquest treball introduïm la classe de "multi-sided Böhm-Bawerk assignment games", que generalitza la coneguda classe de jocs d’assignació de Böhm-Bawerk bilaterals a situacions amb un nombre arbitrari de sectors. Trobem els extrems del core de qualsevol multi-sided Böhm-Bawerk assignment game a partir d’un joc convex definit en el conjunt de sectors enlloc del conjunt de venedors i compradors. Addicionalment estudiem quan el core d’aquests jocs d’assignació és estable en el sentit de von Neumann-Morgenstern.

Assignment markets with the same core

[spa] En el contexto de los juegos de asignación bilaterales, estudiamos el conjunto de matrices asociadas a mercados de asignación con el mismo nucleo. Se proporcionan condiciones sobre las entradas de la matriz que aseguran que los juegos de asignación asociados tienen el mismo núcleo. Se prueba que este conjunto de matrices que dan lugar al mismo núcleo forman un semirretículo con un número finito de elementos minimales y un único máximo. Se da una caracterización de estos elementos minimales. También se proporciona una condición suficiente para obtener un retículo.

Multi-sided Böhm-Bawerk assignment markets: the core

[cat] En aquest treball introduïm la classe de "multi-sided Böhm-Bawerk assignment games", que generalitza la coneguda classe de jocs d’assignació de Böhm-Bawerk bilaterals a situacions amb un nombre arbitrari de sectors. Trobem els extrems del core de qualsevol multi-sided Böhm-Bawerk assignment game a partir d’un joc convex definit en el conjunt de sectors enlloc del conjunt de venedors i compradors. Addicionalment estudiem quan el core d’aquests jocs d’assignació és estable en el sentit de von Neumann-Morgenstern.