The Lorenz-maximal core allocations and the kernel in some classes of assignment games

core, assignment game, lorenz domination, kernel

Egalitarianism in Multi-Choice Games

In this paper we introduce the equal division core for arbitrary multi-choice games and the constrained egalitarian solution for con- vex multi-choice games, using a multi-choice version of the Dutta-Ray algorithm for traditional convex games. These egalitarian solutions for multi-choice games have similar properties as their counterparts for traditional cooperative games. On the class of convex multi-choice games, we axiomatically characterize the constrained egalitarian solu- tion.Multi-choice games;Convex games;Equal division core;Constrained egalitarian solution

Stability and Fairness in Models with a Multiple Membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus.Stability, Fairness, Membership, Coalition Formation

Stability and fairness in models with a multiple membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are in- divisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness on metric environments with indivisible projects. To do so, we explore, among other things, the performance of several well-known solutions (such as the Shapley value, the nucleolus, or the Dutta-Ray value) in these environments.stability, fairness, membership, coalition formation

A Reply to Ponte et al (2016) Supply Chain Collaboration: Some Comments on the Nucleolus of the Beer Game

Purpose: The aim of the paper is to pick up the result of a previously published paper in order to deepen the discussion. We analyze the solution against the background of some well-known concepts and we introduce a newer one. In doing so we would like to inspire the further discussion of supply chain collaboration. Design/methodology/approach: Based on game theoretical knowledge we present and compare seven properties of fair profit sharing. Findings: We show that the nucleolus is a core-solution, which does not fulfil aggregate monotonicity. In contrast the Shapley value is an aggregate monotonic solution but does not belong to the core of every cooperative game. Moreover, we present the Lorenz dominance as an additional fairness criteria. Originality/value: We discuss the very involved procedure of establishing lexicographic orders of excess vectors for games with many players.Peer Reviewe

Stability and Fairness in Models with a Multiple Membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus.Stability, Fairness, Membership, Coalition Formation

Implementing with veto players: a simple non cooperative game

The paper adapts a non cooperative game presented by Dagan, Serrano and Volij (1997) for bankruptcy problems to the context of TU veto balanced games. We investigate the relationship between the Nash outcomes of a noncooperative game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.

Egalitarian distributions in coalitional models: The Lorenz criterion

The paper presents a framework where the most important single-valued solutions in the literature of TU games are jointly analyzed. The paper also suggests that similar frameworks may be useful for other coalitional models.We are grateful for financial support provided by projects PB-96-1469-C-05-04 and BEC2000-0875 of the Spanish Ministry of Education and Science and project UPV00031.321-HA-7903/2000 of the University of The Basque Country

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

Egalitarianism in Multi-Choice Games

In this paper we introduce the equal division core for arbitrary multi-choice games and the constrained egalitarian solution for con- vex multi-choice games, using a multi-choice version of the Dutta-Ray algorithm for traditional convex games. These egalitarian solutions for multi-choice games have similar properties as their counterparts for traditional cooperative games. On the class of convex multi-choice games, we axiomatically characterize the constrained egalitarian solu- tion