Values for rooted-tree and sink-tree digraphs games and sharing a river

We introduce values for rooted-tree and sink-tree digraph games axiomatically and provide their explicit formula representation. These values may be considered as natural extensions of the lower equivalent and upper equivalent solutions for line-graph games studied in Brink, Laan, and Vasil'ev (2007). We study the distribution of Harsanyi dividends. We show that the problem of sharing a river with a delta or with multiple sources among different agents located at different levels along the riverbed can be embedded into the framework of a rooted-tree or sink-tree digraph game correspondingly

The prenucleolus for games with communication structures

It is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented

The prenucleolus for games with communication structures

t is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.TU game; solution concept; communication and conference structure; nucleolus

On 1-convexity and nucleolus of co-insurance games

The situation, in which an enormous risk is insured by a number of insurance companies, is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we show that a co-insurance game possesses several interesting properties that allow to study the nonemptiness and the structure of the core and to construct an efficient algorithm for computing the nucleolus

Semiproportional Values for TU Games.

The goal of the paper is to introduce a family of values for transferable utility cooperative games that are proportional for two- person games and as well satisfying some combinatorial structure com- posed by contributions of complementary coalitions or, to less extent, marginal contributions by players.cooperative TU game; value; proportional sharing; probabilistic model

Marginalist and Efficient Value for TU Games

Abstract We derive an explicit formula for a marginalist and efficient value for TU game which possesses the null-player property and is either continuous or monotonic. We show that every such value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic values possessing the null-player property coincides with the set of random-order values, and, thereby, the last statement provides an axiomatization without the linearity axiom for the latter which is similar to that of Young for the Shapley value. Another axiomatization without linearity for random-order values is provided by marginalism, efficiency, monotonicity and covariance

Shapley value for constant-sum games

cooperative TU game, value, axiomatic characterization, Shapley value,