A characterization of a new value and an existing value for cooperative games with levels structure of cooperation

En aquest treball presentem dues caracteritzacions de dos valors diferents en el marc dels jocs coalicionals amb cooperació restringida. Les restriccions són introduïdes com una seqüència finita de particions del conjunt del jugadors, de manera que cada una d'elles eés més grollera que l'anterior, formant així una estructura amb diferents nivells d'unions a priori.

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

On the nucleolus of 2 x 2 assignment games

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.

Aggregate monotonic stable single-valued solutions for cooperative games

[cat] En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.

The maximun and the addition of assigment games

[cat] En el context dels mercats a dues bandes, considerem, en primer lloc, que els jugadors poden escollir on dur a terme les seves transaccions. Mostrem que el joc corresponent a aquesta situació, que es representa pel màxim d’un conjunt finit de jocs d’assignació, pot ser un joc no equilibrat. Aleshores proporcionem condicions per a l’equilibri del joc i, per aquest cas, analitzem algunes propietats del core del joc. En segon lloc, considerem que els jugadors poden fer transaccions en diversos mercats simultàniament i, llavors, sumar els guanys obtinguts. El joc corresponent, representat per la suma d’un conjunt finit de jocs d’assignació, és equilibrat. A més a més, sota certes condicions, la suma dels cores dels dos jocs d’assignació coincideix amb el core del joc suma.

English grammar games in primary education

The purpose of this study was to analyse pupils’ English grammar acquisition from competitive and cooperative approaches. After searching a wide range of authors’ contribution to English language learning, grammar acquisition, classroom environment and language games. A hundred and twenty pupils from three schools; two from Ripoll and one from Campdevànol were enrolled in a specific grammar games intervention. This was imparted in three different phases: first of all, I interviewed the three teachers from the three schools, then I put into practice my competitive and cooperative games which I designed especially for this study (all the sessions were carried, assessed and registered by myself); finally, all pupils answered a questionnaire related to their experiences in my grammar games intervention. Analysis of teaching interventions showed that, in terms of English language acquisition, pupils used different strategies to show up understanding and achieve the objective of the game such as: recalling their background knowledge, expressing sentences influenced by their internal language and their mother tongue. Data collected revealed that most difficulties were founded in team work, even more in competitive games. The results also showed that team work is something which has to be developed step by step in order to achieve language learning and all pupils’ active participation successfully.

On reduced games and the lexmax solution

For a family of reduced games satisfying a monotonicity property, we introduced the reduced equal split-off set, an extension of the equal split-off set (Branzei et. al, 2006), and study its relation with the core. Regardless of the reduction operation we consider, the intersection between both sets is either empty or a singleton containing the lexmax solution (Arin et al., 2008). We also provide a procedure for computing the lexmax solution for a class of games that includes games with large core (Sharkey, 1982). [JEL Classification: C71]

The Banzhaf Value in the Presence of Externalities

[eng] We propose two generalizations of the Banzhaf value for partition function form games. In both cases, our approach is based on probability distributions over the set of possible coalition structures that may arise for any given set of agents. First, we introduce a family of values, one for each collection of the latter probability distributions, defined as the Banzhaf value of an expected coalitional game. Then, we provide two characterization results for this new family of values within the framework of all partition function games. Both results rely on a property of neutrality with respect to amalgamation of players. Second, as this collusion transformation fails to be meaningful for simple games in partition function form, we propose another generalization of the Banzhaf value which also builds on probability distributions of the above type. This latter family is characterized by means of a neutrality property which uses an amalgamation transformation of players for which simple games are closed.

The Banzhaf Value in the Presence of Externalities

[eng] We propose two generalizations of the Banzhaf value for partition function form games. In both cases, our approach is based on probability distributions over the set of possible coalition structures that may arise for any given set of agents. First, we introduce a family of values, one for each collection of the latter probability distributions, defined as the Banzhaf value of an expected coalitional game. Then, we provide two characterization results for this new family of values within the framework of all partition function games. Both results rely on a property of neutrality with respect to amalgamation of players. Second, as this collusion transformation fails to be meaningful for simple games in partition function form, we propose another generalization of the Banzhaf value which also builds on probability distributions of the above type. This latter family is characterized by means of a neutrality property which uses an amalgamation transformation of players for which simple games are closed.

Os games digitais como um recurso cognitivo para o ensino da historia da Catalunha: um estudo de caso

Os games digitais possuem um valor educativo importante e têm sido reconhecidos pelos educadores como um rico e produtivo espaço que proporciona conteúdos de aprendizagem para os estudantes, melhorando, através dele, o desenvolvimento cognitivo do aluno. Este artigo explora as oportunidades cognitivas dos games digitais como uma ferramenta de aprendizagem e mostra um estudo de caso: o jogo de Joan de Peratallada. O objetivo desse estudo é promover o diálogo e a possível colaboração entre um jogo digital cognitivo aplicado as escolas primárias de forma a colaborar com a ensino de historia de Catalunha, Espanha.

The pedagogical value of games and songs : The perceptions of teachers

Aquest estudi intenta explorar i descobrir les actituds i creences d’alguns mestres de llengua anglesa de Catalunya sobre la naturalesa dels jocs i les cançons, així com el paper que juguen en les seves aules per ensenyar l’anglès als infants. Les opinions dels mestres de llengua anglesa van ser recollides mitjançant un qüestionari que contenia preguntes sobre els jocs i les cançons i els resultats s’analitzen i s’exposen en aquest estudi.

On the (in)compatibility of rationality, monotonicity and consistency for cooperative games

On the domain of cooperative transferable utility games, we investigate if there are single valued solutions that reconcile rationality, consistency and monotonicity (with respect to the worth of the grand coalition) properties. This paper collects some impossibility results on the combination of core selection with either complement or projected consistency, and core selection, max consistency and monotonicity. By contrast, possibility results show up when combining individual rationality, projected consistency and monotonicity.