In this paper, we introduce two polytopes that respect a digraph in the sense that for every vector in the polytope every component corresponds to a node and is at least equal to the component corresponding to each successor of this node. The sharing polytope is the set of all elements from the...

In this paper, we consider the relationship between the Weber set and the Shapley set being the set of all weighted Shapley values of a TU-game. In particular, we propose a new proof for the fact that the Weber set always includes the Shapley set. It is shown that the inclusion mentioned follows...

Semivalues like the Shapley value and the Banzhaf value may assign the same payoff vector to different games. It is even possible that two games attain the same outcome for all semivalues. Due to the linearity of the semivalues, this exactly occurs in case the difference of the two games is an...

We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the...

A Harsanyi payoff vector (see Vasil’ev in Optimizacija Vyp 21:30–35, 1978) of a cooperative game with transferable utilities is obtained by some distribution of the Harsanyi dividends of all coalitions among its members. Examples of Harsanyi payoff vectors are the marginal contribution...

We study a non-cooperative model of unilateral network formation. Derks et al. [2008b] prove the existence of local-Nash and global-Nash networks for games with payoff functions that satisfy a framework of axiomatic properties. These properties are inspired by the one-way flow model, which is...