The core of games on distributive lattices : how to share benefits in a hierarchy

Finding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the most popular solution concept since it is based on some rationality condition. In many real situations, not all possible coalitions can form, so that classical TU-games cannot be used. An interesting case is when possible coalitions are defined through a partial ordering of the players (or hierarchy). Then feasible coalitions correspond to teams of players, that is, one or several players with all their subordinates. In these situations, it is not obvious to define a suitable notion of core, reflecting the team structure, and previous attempts are not satisfactory in this respect. We propose a new notion of core, which imposes efficiency of the allocation at each level of the hierarchy, and answers the problem of sharing benefits in a hierarchy. We show that the core we defined has properties very close to the classical case, with respect to marginal vectors, the Weber set, and balancedness.Cooperative game, feasible coalition, core, hierarchy.

A new approach to the core and Weber set of multichoice games

Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that the set of imputations may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex compact set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their coincidence in the convex case remain valid. A last section makes a comparison with the core defined by van den Nouweland et al.multichoice game ; lattice ; core

The core of bicapacities and bipolar games

Bicooperative games generalize classical cooperative games in the sense that a player is allowed to play in favor or against some aim, besides non participation. Bicapacities are monotonic bicooperative games, they are useful in decision making where underlying scales are of bipolar nature, i.e., they distinguish between good/satisfactory values and bad/unsatisfactory ones. We propose here a more general framework to represent such situations, called bipolar game. We study the problem of finding the core of such games, i.e., theset of additive dominating games.fuzzy measure, bicapacity, cooperative game, bipolar scale,core

The core of games on k-regular set systems

In the classical setting of cooperative game theory, it is always assumed that all coalitions are feasible. However in many real situations, there are restrictions on the set of coalitions, for example duo to communication, order or hierarchy on the set of players, etc. There are already many works dealing with games on restricted set of coalitions, defining many different structures for the set of feasible coalitions, called set systems. We propose in this paper to consider k-regular set systems, that is, set systems having all maximal chains of the same length k. This is somehow related to communication graphs. We study in this perspective the core of games defined on k-regular set systems. We show that the core may be unbounded and without vertices in some situations.Cooperative game ; feasible coalition ; core

The core of bicapacities and bipolar games

Selected papers from IFSA 2005, 11th World Congress of International Fuzzy Systems Association - Beijing, China, 28-31 July 2005 ED EPSInternational audienceBicooperative games generalize classical cooperative games in the sense that a player is allowed to play in favor or against some aim, besides non participation. Bicapacities are monotonic bicooperative games, they are useful in decision making where underlying scales are of bipolar nature, i.e., they distinguish between good/satisfactory values and bad/unsatisfactory ones. We propose here a more general framework to represent such situations, called bipolar game. We study the problem of finding the core of such games, i.e., theset of additive dominating games

The restricted core of games on distributive lattices: how to share benefits in a hierarchy

ED EPSInternational audienceFinding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the most popular solution concept since it is based on some rationality condition. In many real situations, not all possible coalitions can form, so that classical TU-games cannot be used. An interesting case is when possible coalitions are defined through a partial ordering of the players (or hierarchy). Then feasible coalitions correspond to teams of players, that is, one or several players with all their subordinates. In these situations, the core in its usual formulation may be unbounded, making its use difficult in practice. We propose a new notion of core, called the restricted core, which imposes efficiency of the allocation at each level of the hierarchy, is always bounded, and answers the problem of sharing benefits in a hierarchy. We show that the core we defined has properties very close to the classical case, with respect to marginal vectors, the Weber set, and balancedness

A new approach to the core and Weber set of multichoice games

ED EPSInternational audienceMultichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that the set of imputations may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex compact set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their coincidence in the convex case remain valid. A last section makes a comparison with the core defined by van den Nouweland et al

Le coeur des jeux sur des ensembles ordonnés

Le domaine de la théorie des jeux coopératifs s'est enrichi récemment de plusieurs nouveaux types de jeux, essayant de modéliser plus précisément le comportement des joueurs dans une situation réelle. Au sens classique, pour un ensemble N de n joueurs, un jeu coopératif a chaque coalition de joueurs. A un nombre v(A) représentant le résultat (somme d'argent, bénéfice au sens général, etc.) qu'aura cette coalition si le jeu est joué. Pour un jeu coopératif, un problème central est si tous les joueurs de N d'accords de jouer ensemble. Donc on doit trouver une façon équitable de partager la somme v(N) entre tous les joueurs, une des solutions s'appelle le coeur du jeu. Un jeu coopératif au sens classique est défini sur l'ensemble de toutes le coalitions. Si on impose quelques restrictions sur les coalitions, on peut obtenir un jeu sur une collection de certains sous-ensembles de N, dites coalitions réalisables. On retrouve ainsi bon nombre de cas particuliers (jeux classiques, jeux distributifs, jeux k-réguliers). Cette thèse a essentiellement porté sur des propriétés du cœur des jeux sur des ensembles ordonnés. On considère des jeux multi-choix, jeux bipolaires, jeux distributifs et jeux k-réguliers. Nous avons étudié en particulier la structure géométrique du coeur, ainsi que les conditions nécessaires et suffisantes de non vacuité du coeur . Dans beaucoup de cas, les résultats obtenus ont généralisé de manière naturelle les grands résultats classiques.PARIS1-BU Pierre Mendès-France (751132102) / SudocPARIS1-CNRS-Maison des sc. éco (751055202) / SudocSudocFranceF

Laser consolidation - a rapid manufacturing process for making net-shape functional components

Laser consolidation is a novel rapid manufacturing process that produces a net-shape functional complex part layer by layer directly from a CAD model without any moulds or dies. This process uses a laser beam to melt a controlled amount of injected powder on a base plate to deposit the first layer and on previous passes for the subsequent layers. As opposed to conventional machining processes, this computer-aided manufacturing (CAM) technology builds complete net-shape functional parts or features on an existing component by adding instead of removing material. The LC samples also show very good surface finish and dimensional accuracy. Surface finish of the order of 1~2 \ub5m (Ra) is obtained on as-consolidated IN-625. In this paper, laser consolidation process will be introduced, the functional properties of the laser-consolidated IN-625 and Ti-6Al-4V alloys will be described, and two applications of the process will be discussed.Peer reviewed: YesNRC publication: Ye

Laser consolidation - a one-step manufacturing process for making net-shape functional aerospace components

Laser consolidation (LC) is an emerging novel computer-aided manufacturing process that produces net-shaped functional parts layer by layer directly from a CAD model, by using a laser beam to melt the injected powder and re-solidifying it on the previous pass. As an alternative to the conventional machining process, this novel manufacturing process builds parts or features on an existing part by adding instead of removing material. In this paper, functional properties of laser consolidated IN-625, IN-738, Ti-6Al-4V and Al-4047 alloys will be reported. The laser consolidated materials exhibit the mechanical properties comparable to respective wrought materials. The examples of laser consolidation for making net-shaped functional components for aerospace applications will also be reported.Peer reviewed: YesNRC publication: Ye