The approximate f-core and the utopia payoff for infinite assignment games

Assignment problems where both sets of agents are countably infinite, the so-called infinite assignment problems, are studied as well as the related assignment games. Further, two solutions for these games are studied. The first one is the approximate f-core for games with a finite value. This particular solution takes into account that due to organisational limitations only finite groups of agents can protest against proposals of profit distributions. Second, we study the utopia payoff, the perfect proposal in which each agent receives the maximal amount he can get. \u

Van der Waals spin valves

We propose spin valves where a 2D non-magnetic conductor is intercalated between two ferromagnetic insulating layers. In this setup, the relative orientation of the magnetizations of the insulating layers can have a strong impact on the in-plane conductivity of the 2D conductor. We first show this for a graphene bilayer, described with a tight-binding model, placed between two ferromagnetic insulators. In the anti-parallel configuration, a band gap opens at the Dirac point, whereas in the parallel configuration, the graphene bilayer remains conducting. We then compute the electronic structure of graphene bilayer placed between two monolayers of the ferromagnetic insulator CrI$_3$, using density functional theory. Consistent with the model, we find that a gap opens at the Dirac point only in the antiparallel configuration.Comment: 5 pages, 4 figure

Convex Games with Countable Number of Players and Sequencing Situations

AMS classification: 91A12;Cooperative games;countable number of players;convexity;infinite sequencing situations

Multi-Choice Total Clan Games: Characterizations and Solution Concepts

This paper deals with a new class of multi-choice games, the class of multi- choice total clan games. The structure of the core of a multi-choice clan game is explicitly described. Furthermore, characterizations of multi-choice total clan games are given and bi-monotonic allocation schemes related to players' levels are introduced for such games. It turns out that some elements in the core of a multi- choice total clan game are extendable to such bi-monotonic allocation schemes via suitable compensation-sharing rules on the domain of multi-choice (total) clan games.Multi-choice games;Clan games;Monotonic allocation schemes

The Owen Set and the Core of Semi-Infinite Linear Production Situations

AMS classifications: 90D12, 90C05, 90C34.cooperative games;linear production;core;duality gap

On the Core of Semi-Infinite Transportation Games with Divisible Goods

AMS classifications: 90D12; 90C05; 90C34;cooperative games

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

A Technical Note on Lorenz Dominance in Cooperative Games

AMS classification: 91A12Cooperative games;Lorenz dominance;egalitarianism;con- strained egalitarian solution;equal split-off set