In this paper cost sharing problems are considered. We focus on problems on a rooted tree, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, we call these games irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games (Littlechil...

Abstract: This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (∗)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (∗)-antimonotonicity by ...

A set of necessary and sufficient conditions for convexity of a transferable utility game in terms of its decomposition into unanimity games is shown to be minimal: none of the conditions is redundant. The result is used to provide an axiomatization of the Shapley value on the set of convex games.

We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of E¢ ciency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition ...

We introduce the notion of Burkill-Cesari (BC) differentiability for transferable utility (TU) games and compare it with some other analogous established notions existing in cooperative game theoretical literature. We also apply our notion to the study of the core of a new class of TU games.

In this paper we propose a characterization of the coalitional value for transferable utility games (Owen, 1977), and we define and study coalitional semivalues, which are generalizations of semivalues (Dubey, Neyman and Weber, 1981).

The goal of the paper is to introduce a family of values for transferable utility cooperative games that are proportional for twoperson games and as well satisfying some combinatorial structure composed by contributions of complementary coalitions or, to less extent, marginal contributions by players.

The nucleon is introduced as a new allocation concept for non-negative cooperative n-person transferable utility games. The nucleon may be viewed as the multiplicative analogue of Schmeidler's nucleolus. It is shown that the nucleon of (not necessarily bipartite) matching games can be computed in polynomial time. 9 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

The consistent value is an extension of the Shapley value to the class of games with non-transferable utility. In this paper, the consistent value will be characterized for market games with a continuum of players of two types. We will show that for such games the consistent value need not belong to the core, and provide conditions under which there is equivalence between the two concepts.