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.

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.

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

Security strategies and equilibria in multiobjetives matrix games

Multiobjective matrix games have been traditionally analyzed from two different points of view: equiibrium concepts and security strategies. This paper is based upon the idea that both players try to reach equilibrium points playing pairs of security strategies, as it happens in scalar matrix games. We show conditions guaranteeing the existence of equilibria in security strategies, named security equilibria

All assignment games with the same core have the same nucleolus

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representative

LEVERAGING SANDBOX IMMERSIVE 3D VIRTUAL WORLDS TO DEVELOP DO-IT- YOURSELF TEACHING GAMES: IMPLEMENTATION TO MARKETING CASE STUDY TEACHING IN SECOND LIFE

Games are powerful and engaging. On average, one billion people spend at least 1 hour a day playing computer and videogames. This is even more true with the younger generations. Our students have become the < digital natives >, the < gamers >, the < virtual generation >. Research shows that those who are most at risk for failure in the traditional classroom setting, also spend more time than their counterparts, using video games. They might strive, given a different learning environment. Educators have the responsibility to align their teaching style to these younger generation learning styles. However, many academics resist the use of computer-assisted learning that has been "created elsewhere". This can be extrapolated to game-based teaching: even if educational games were more widely authored, their adoption would still be limited to the educators who feel a match between the authored games and their own beliefs and practices. Consequently, game-based teaching would be much more widespread if teachers could develop their own games, or at least customize them. Yet, the development and customization of teaching games are complex and costly. This research uses a design science methodology, leveraging gamification techniques, active and cooperative learning theories, as well as immersive sandbox 3D virtual worlds, to develop a method which allows management instructors to transform any off-the-shelf case study into an engaging collaborative gamified experience. This method is applied to marketing case studies, and uses the sandbox virtual world of Second Life. -- Les jeux sont puissants et motivants, En moyenne, un milliard de personnes passent au moins 1 heure par jour jouer à des jeux vidéo sur ordinateur. Ceci se vérifie encore plus avec les jeunes générations, Nos étudiants sont nés à l'ère du numérique, certains les appellent des < gamers >, d'autres la < génération virtuelle >. Les études montrent que les élèves qui se trouvent en échec scolaire dans les salles de classes traditionnelles, passent aussi plus de temps que leurs homologues à jouer à des jeux vidéo. lls pourraient potentiellement briller, si on leur proposait un autre environnement d'apprentissage. Les enseignants ont la responsabilité d'adapter leur style d'enseignement aux styles d'apprentissage de ces jeunes générations. Toutefois, de nombreux professeurs résistent lorsqu'il s'agit d'utiliser des contenus d'apprentissage assisté par ordinateur, développés par d'autres. Ceci peut être extrapolé à l'enseignement par les jeux : même si un plus grand nombre de jeux éducatifs était créé, leur adoption se limiterait tout de même aux éducateurs qui perçoivent une bonne adéquation entre ces jeux et leurs propres convictions et pratiques. Par conséquent, I'enseignement par les jeux serait bien plus répandu si les enseignants pouvaient développer leurs propres jeux, ou au moins les customiser. Mais le développement de jeux pédagogiques est complexe et coûteux. Cette recherche utilise une méthodologie Design Science pour développer, en s'appuyant sur des techniques de ludification, sur les théories de pédagogie active et d'apprentissage coopératif, ainsi que sur les mondes virtuels immersifs < bac à sable > en 3D, une méthode qui permet aux enseignants et formateurs de management, de transformer n'importe quelle étude de cas, provenant par exemple d'une centrale de cas, en une expérience ludique, collaborative et motivante. Cette méthode est appliquée aux études de cas Marketing dans le monde virtuel de Second Life.

Blood corticosterone levels and intersexual selection games: best-of-bad-job strategies of male common lizards

Glucocorticoids affect physiology and behaviour, reproduction and potentially sexual selection as well. Shortterm and moderate glucocorticoid elevations are suggested to be adaptive, and prolonged and high elevations may be extremely harmful. This suggests that optimal reproductive strategies, and thus sexual selection, may be dose dependent. Here, we investigate effects of moderate and high elevations of blood corticosterone levels on intra- and intersexual behaviour and mating success of male common lizards Lacerta vivipara. Females showed less interest and more aggressive behaviour towards high corticosterone males and blood corticosterone levels affected male reproductive strategy. Males of moderate and high corticosterone elevations, compared with Control males, showed increased interest (i.e., higher number of chases, tongue extrusions, and approaches) towards females and high corticosterone males initiated more copulation attempts. However, neither increased male interest nor increased copulation attempts resulted in more copulations. This provides evidence for a best-of-a-bad-job strategy, where males with higher corticosterone levels compensated for reduced female interest and increased aggressive female behaviour directed towards them, by showing higher interest and by conducting more copulation attempts. Blood corticosterone levels affected intrasexual selection as well since moderate corticosterone levels positively affected male dominance, but dominance did not affect mating success. These findings underline the importance of female mate choice and are in line with adaptive compensatory behaviours of males. They further show that glucocorticoid effects on behaviour are dose dependent and that they have important implications for sexual selection and social interactions, and might potentially affect Darwinian fitness.

Consumer Advisory Bulletin, Work-at-Home Scams:So You Didn’t Order That? Protecting yourself from unauthorized credit card charges, August 2012

The Attorney General’s Consumer Protection Division receives hundreds of calls and consumer complaints every year. Follow these tips to avoid unexpected expense and disappointments. This record is about: So You Didn’t Order That? Protecting yourself from unauthorized credit card charges

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

Security strategies and equilibria in multiobjetives matrix games

Multiobjective matrix games have been traditionally analyzed from two different points of view: equiibrium concepts and security strategies. This paper is based upon the idea that both players try to reach equilibrium points playing pairs of security strategies, as it happens in scalar matrix games. We show conditions guaranteeing the existence of equilibria in security strategies, named security equilibria