Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Further- more, (level-increase) monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is ex- tendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game.Multi-choice games;Convex games;Marginal games;Weber set;Monotonic allocation schemes.

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

Ensuring the boundedness of the core of games with restricted cooperation

The core of a cooperative game on a set of players N is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection F of 2N), the core may become unbounded, which makes it usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem : can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded ? The new core obtained is called the restricted core. We completely solve the question when F is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case.Cooperative game, core, restricted cooperation, bounded core, Weber set.

The Average Tree Solution for Multi-choice Forest Games

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al. [2008] for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.Average tree solution; Communication graph; (pre-)Core; Hierarchical outcomes; Multi-choice games.

Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Further- more, (level-increase) monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is ex- tendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game

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

Convex Games versus Clan Games

In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games.We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games.Furthermore, each monotonic convex game generates a total clan game with zero worth for the clan by a "dualize and extend" procedure.These procedures are also useful for relating core elements and elements of the Weber set of the corresponding games.convex games;core;dual games;marginal games;total clan games;Weber set