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 buyerseller exact representative.core, nucleolus, assignment game, kernel

The assignment game: core bounds for mixe-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyerseller exact games and satisfy the condition that each mixedpair 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 buyerseller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixedpair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a 45olattice by means of the core of an assignment game can now be answered.core, exact games, assignment 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.core, assignment game, core dimension

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.convex games, assignment game, core

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 representativeExisteixen jocs cooperatius d'utilitat transferible que tot i tenir el mateix core tenen diferent nucleolus. En aquest treball es mostra que això no pot passar amb els jocs d'assignaciò és a dir que, en aquests jocs, el nucleolus ve determinat pel core del joc i per tant dos jocs d'assignació amb el mateix core tenen forçosament el mateix nucleolus. Per provar-ho mostrem que el nucleolus d'un joc d'assignació coincideix amb el de l'únic joc que el representa amb la propietat de ser 'buyer-seller' exact

Plant hormone signaling during development: insights from computational models

International audienceRecent years have seen an impressive increase in our knowledge of the topology of plant hormone signaling networks. The complexity of these topologies has motivated the development of models for several hormones to aid understanding of how signaling networks process hormonal inputs. Such work has generated essential insights into the mechanisms of hormone perception and of regulation of cellular responses such as transcription in response to hormones. In addition, modeling approaches have contributed significantly to exploring how spatio-temporal regulation of hormone signaling contributes to plant growth and patterning. New tools have also been developed to obtain quantitative information on hormone distribution during development and to test model predictions, opening the way for quantitative understanding of the developmental roles of hormones. ⺠Plant hormone signaling pathways exhibit complex topologies. ⺠Computational models predict the dynamics of hormone signaling. ⺠Modeling provides key insights on the role of hormones during growth and development. ⺠New tools allow for a quantitative understanding of hormone signaling

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

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 nucleolusEls jocs d'assignació amb preu uniforme són aquells mercats d'assignació on el core es redueix a un segment. En aquests casos, per a tots els agents actius en el mercat, els preus competitius varien de forma uniforme, tot i que els productes poden ser no homogenis. En aquest treball es dona una caracterització dels mercats amb preu uniforme a partir de la matriu d'assignació Els únics mercats on tots els subjocs són de preu uniforme són els mercats de cavalls de Bohm-Bawerk. Finalment,provem que en aquests mercats de preu uniforme el kernel, o conjunt de pagaments que s'obtenen a partir d'un procés de negociació bilateral i simètric, o bé coincideix amb tot core o es redueix al seu punt mig que és el nucleolus

Stable cores in information graph games

In an information graph situation, a finite set of agents and a source are the set of nodes of an undirected graph with the property that two adjacent nodes can share information at no cost. The source has some information (or technology), and agents in the same component as the source can reach this information for free. In other components, some agent must pay a unitary cost to obtain the information. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if and only if the information graph is cycle-complete, or equivalently if the game is concave. Otherwise, whether there always exists a stable set is an open question. If the information graph consists of a ring that contains the source, a stable set always exists and it is the core of a related situation where one edge has been deleted

Stable cores in information graph games

Stable cores in information graph games Abstract: In an information graph situation, some agents that are connected by an undirected graph can share with no cost some information or technology that can also be obtained from a source. If an agent is not connected to an informed player, this agent pays a unitary cost to obtain this technology. A coalitional cost game can be defined from this situation, and the core of this game is known to be non- empty. We prove that the core of an information graph game is a von Neumann-Morgenstern stable set if and only if the graph is cycle- complete, or equivalently if the information graph game is concave. When the graph is not cycle-complete, whether there always exists a stable set is an open question. In this regard, we show that if the information graph consists of a ring that contains the source, then a stable set always exists and it is the core of a related information graph situation where one edge has been deleted