Axiomatization of the nucl eolus of assignment games

On the domain of general assignment games (with possible reservation prices) the core is axiomatized as the unique solution satisfying two consistency principles: projection consistency and derived consistency. Also, an axiomatic characterization of the nucleolus is given as the unique solution that satisfies derived consistency and equal maximum complaint between groups. As a consequence, we obtain a geometric characterization of the nucleolus. Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his / her optimally matched partner equals the maximum amount that he / she can receive from this partner, also remaining inside the core. We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions. Key words: cooperative games, assignment game, core, nucleolus

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]

Cooperative games with size-truncated information

[Eng] We study the marginal worth vectors and their convex hull, the socalled Weber set, from the original coalitional game and the transformed one, which is called the Weber set of level k. We prove that the core of the original game is included in each of the Weber set of level k, for any k, and that the Weber sets of consecutive levels form a chain if and only if the original game is 0-monotone. Even if the game is not 0-monotone, the intersection of the Weber sets for consecutive levels is always not empty, what is not the case for non-consecutive ones. Spanish education system.

Cooperative games with size-truncated information

[Eng] We study the marginal worth vectors and their convex hull, the socalled Weber set, from the original coalitional game and the transformed one, which is called the Weber set of level k. We prove that the core of the original game is included in each of the Weber set of level k, for any k, and that the Weber sets of consecutive levels form a chain if and only if the original game is 0-monotone. Even if the game is not 0-monotone, the intersection of the Weber sets for consecutive levels is always not empty, what is not the case for non-consecutive ones. Spanish education system.

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.

Singing Desire : erotismo y deseo en las canciones para laúd en Inglaterra, 1597-1615

Las canciones para laúd o ayres en la Inglaterra de finales del siglo XVI y principios del XVII además de ser un género muy importante dentro de la música inglesa, son una manifestación cultural de varios ámbitos, tales como patronaje, comercio, género, clase social, filosofía y religión. Con sus letras eróticas en combinación con la voz solista, la música del laúd y la viola da gamba, fueron un medio de expresión muy intenso que permitía la entrada a un universo de sentimiento, pero que también representaba un pensamiento filosófico y una conciencia retórica. Basado en estudios previos, este ensayo explora las ayres desde diferentes ámbitos: el social, el de género, el humanista y el literario para entender el género de las ayres a fondo de manera que le sea útil al intérprete al momento de abordar este repertorio.

Enjoying cooperative games: The R package GameTheory

This paper focuses on cooperative games with transferable utility. We propose the computation of two solutions, the Shapley value for n agents and the nucleolus with a maximum of four agents. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud and the random arrival rules. Keywords: Cooperative game, Shapley value, nucleolus, claims problem, claims rule, bankruptcy.

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.

Parallel characterizations of a generalized shapley value and a generalized banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.

A characterization of cooperative TU-games with large monotonic core

[cat] El concepte de joc cooperatiu amb large core és introduït per Sharkey (1982) i el de Population Monotonic Allocation Scheme és definit per Sprumont (1990). Inspirat en aquests conceptes, Moulin (1990) introdueix la noció de large monotonic core donant una caracterització per a jocs de tres jugadors. En aquest document provem que tots els jocs amb large monotonic core són convexes. A més, donem un criteri efectiu per determinar si un joc té large monotonic core o no, i daquí obtenim una caracterització pel cas de quatre jugadors.

A characterization of cooperative TU-games with large monotonic core

[cat] El concepte de joc cooperatiu amb large core és introduït per Sharkey (1982) i el de Population Monotonic Allocation Scheme és definit per Sprumont (1990). Inspirat en aquests conceptes, Moulin (1990) introdueix la noció de large monotonic core donant una caracterització per a jocs de tres jugadors. En aquest document provem que tots els jocs amb large monotonic core són convexes. A més, donem un criteri efectiu per determinar si un joc té large monotonic core o no, i daquí obtenim una caracterització pel cas de quatre jugadors.

Some Notes and Comments on the Efficient use of Information in Repeated Games with Poisson Signals

In the present paper we characterize the optimal use of Poisson signals to establish incentives in the "bad" and "good" news models of Abreu et al. [1]. In the former, for small time intervals the signals' quality is high and we observe a "selective" use of information; otherwise there is a "mass" use. In the latter, for small time intervals the signals' quality is low and we observe a "fine" use of information; otherwise there is a "non-selective" use. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Public Monitoring, Infor- mation Characteristics.

El canto coral y las orquestas infantiles, una educación en valores = Choir singing and children’s orchestras, an education in values

This article looks at the musical activity carried out at Palafrugell Music School as a musical education centre over the past forty years. After giving a brief description of the work carried out there by vocal and instrumental groups, the article analyses and offers examples and tangible motives that use activities to show that forming part of a coral or instrumental group helps personal development and promotes the acquisition of habits, alongside musical training and learning. In short, an education in values