Semi-Infinite Assignment Problems and Related Games

In 1972 Shapley and Shubik introduced assignment games associated to finite assignment problems in which two types of agents were involved and they proved that these games have a non-empty core. In this paper we look at the situation where the set of one type is infinite and investigatewhen the core of the associated game is non-empty. Two infinite programming problems arise here, which we tackle with the aid of finite approximations. We prove that there is no duality gap and we show that the core of the corresponding game is non-empty. Finally, the existence of optimal assignments is discussed.Infinite programs;assignment;cooperative games;balancedness

Games Arising from Infinite Production Situations

AMS classifications: 90D12, 90C05.linear semi-infinite programs;linear transformation;cooperative games;balancedness

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

Convex Games with Countable Number of Players and Sequencing Situations

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

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

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

A Technical Note on Lorenz Dominance in Cooperative Games

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

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