Multi-sided Böhm-Bawerk assignment markets: the nucleolus and the core-center

En aquest treball mostrem que, a diferència del cas bilateral, per als mercats multilaterals d'assignació coneguts amb el nom de Böhm-Bawerk assignment games, el nucleolus i el core-center, i. e. el centre de masses del core, no coincideixen en general. Per demostrar-ho provem que donant un m-sided Böhm-Bawerk assignment game les dues solucions anteriors poden obtenir-se respectivament del nucleolus i el core-center d'un joc convex definit en el conjunt format pels m sectors. Encara més, provem que per calcular el nucleolus d'aquest últim joc només les coalicions formades per un jugador o m-1 jugadors són importants. Aquests resultats simplifiquen el càlcul del nucleolus d'un multi-sided ¿¿ohm-Bawerk assignment market amb un número molt elevat d'agents.

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.

An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

[cat] Aquest treball tracta d’extendre la noció d’equilibri simètric de negociació bilateral introduït per Rochford (1983) a jocs d’assignació multilateral. Un pagament corresponent a un equilibri simètric de negociación multilateral (SMB) és una imputación del core que garanteix que qualsevol agent es troba en equilibri respecte a un procés de negociación entre tots els agents basat en allò que cadascun d’ells podria rebre -i fer servir com a amenaça- en un ’matching’ òptim diferent al que s’ha format. Es prova que, en el cas de jocs d’assignació multilaterals, el conjunt de SMB és sempre no buit i que, a diferència del cas bilateral, no sempre coincideix amb el kernel (Davis and Maschler, 1965). Finalment, responem una pregunta oberta per Rochford (1982) tot introduïnt un conjunt basat en la idea de kernel, que, conjuntament amb el core, ens permet caracteritzar el conjunt de SMB.

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

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

Uniform-price assignment markets

Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolus

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

A fully-automatic caudate nucleus segmentation of brain MRI: application in volumetric analysis of pediatric attention-deficit/hyperactivity disorder

Background Accurate automatic segmentation of the caudate nucleus in magnetic resonance images (MRI) of the brain is of great interest in the analysis of developmental disorders. Segmentation methods based on a single atlas or on multiple atlases have been shown to suitably localize caudate structure. However, the atlas prior information may not represent the structure of interest correctly. It may therefore be useful to introduce a more flexible technique for accurate segmentations. Method We present Cau-dateCut: a new fully-automatic method of segmenting the caudate nucleus in MRI. CaudateCut combines an atlas-based segmentation strategy with the Graph Cut energy-minimization framework. We adapt the Graph Cut model to make it suitable for segmenting small, low-contrast structures, such as the caudate nucleus, by defining new energy function data and boundary potentials. In particular, we exploit information concerning the intensity and geometry, and we add supervised energies based on contextual brain structures. Furthermore, we reinforce boundary detection using a new multi-scale edgeness measure. Results We apply the novel CaudateCut method to the segmentation of the caudate nucleus to a new set of 39 pediatric attention-deficit/hyperactivity disorder (ADHD) patients and 40 control children, as well as to a public database of 18 subjects. We evaluate the quality of the segmentation using several volumetric and voxel by voxel measures. Our results show improved performance in terms of segmentation compared to state-of-the-art approaches, obtaining a mean overlap of 80.75%. Moreover, we present a quantitative volumetric analysis of caudate abnormalities in pediatric ADHD, the results of which show strong correlation with expert manual analysis. Conclusion CaudateCut generates segmentation results that are comparable to gold-standard segmentations and which are reliable in the analysis of differentiating neuroanatomical abnormalities between healthy controls and pediatric ADHD.

Automatic Prediction of Facial Trait Judgments: Appearance vs. Structural Models

Evaluating other individuals with respect to personality characteristics plays a crucial role in human relations and it is the focus of attention for research in diverse fields such as psychology and interactive computer systems. In psychology, face perception has been recognized as a key component of this evaluation system. Multiple studies suggest that observers use face information to infer personality characteristics. Interactive computer systems are trying to take advantage of these findings and apply them to increase the natural aspect of interaction and to improve the performance of interactive computer systems. Here, we experimentally test whether the automatic prediction of facial trait judgments (e.g. dominance) can be made by using the full appearance information of the face and whether a reduced representation of its structure is sufficient. We evaluate two separate approaches: a holistic representation model using the facial appearance information and a structural model constructed from the relations among facial salient points. State of the art machine learning methods are applied to a) derive a facial trait judgment model from training data and b) predict a facial trait value for any face. Furthermore, we address the issue of whether there are specific structural relations among facial points that predict perception of facial traits. Experimental results over a set of labeled data (9 different trait evaluations) and classification rules (4 rules) suggest that a) prediction of perception of facial traits is learnable by both holistic and structural approaches; b) the most reliable prediction of facial trait judgments is obtained by certain type of holistic descriptions of the face appearance; and c) for some traits such as attractiveness and extroversion, there are relationships between specific structural features and social perceptions.

Uniform-price assignment markets

Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolus

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