The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a “partition function”outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show t...

The Shapley value, a solution concept from cooperative game theory, has recently been considered for both unrooted and rooted phylogenetic trees. Here, we focus on the Shapley value of unrooted trees and first revisit the so-called split counts of a phylogenetic tree and the Shapley transformation matrix that allows for the calculation of the Shapley value from the edge lengths of a tree. We sh...

According to the work of Faigle [3] a static Shapley value for games on matroids has been introduced in Bilbao, Driessen, JiménezLosada and Lebrón [1]. In this paper we present a dynamic Shapley value by using a dynamic model which is based on a recursive sequence of static models. In this new model for games on matroids, our main result is that there exists a unique value satisfying analogous ...

We introduce a new axiom, the balanced contributions property for equal contributors. This axiom is defined by restricting the requirement of the balanced contributions property (Myerson (1980)) to two players whose contributions to the grand coalition are the same. We prove that this axiom, together with efficiency and weak covariance, characterizes a new class of solutions, the r-egalitarian ...

The Shapley value and the fair proportion index of phylogenetic trees have been introduced recently for the purpose of making conservation decisions in genetics. Moreover, also very recently, Hartmann (J Math Biol 67:1163-1170, 2013) has presented data which shows that there is a strong correlation between a slightly modified version of the Shapley value (which we call the modified Shapley valu...

Interval Shapley value (ISV) was initially considered for static one-shot games in [1, 2]. In [3, 4] it was shown that the Shapley value in dynamic games is timeinconsistent. To satisfy time-consistency condition for the Shapley value it is necessary to introduce a new control variable, so-called imputation distribution procedure (IDP). The case with interval Shapley value for dynamic games was...

The paper characterizes the position value and the Myerson value for communication situations. The position value is originally defined as the sum of half the Shapley value of the link games but is also represented by the Shapley value of a modification of the link games. That modification is called the divided link games. In addition, by constructing coalition structures of the divided links f...

The Shapley value (Shapley (1953)) is one of the most prominent one-point solution concepts in cooperative game theory that divides revenues (or cost, power) that can be obtained by cooperation of players in the game. The Shapley value is mathematically characterized by properties that have appealing real-world interpretations and hence its use in practical settings is easily justified. The dow...