We study the consequences of a solidarity property that specifies how a value for cooperative games should respond if some player forfeits his productivity, i.e., becomes a null player. Nullified solidarity states that in this case either all players weakly gain together or all players weakly...

If a player is removed from a game, what keeps the payoff of the remaining players unchanged? Is it the removal of a special player or its presence among the remaining players? This article answers this question in a complement study to Kamijo and Kongo (2012). We introduce axioms of invariance...

This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than...

We show that the core of any n-player TU-game with a non-empty core can be accessed with at most n−1 blocks. It turns out that this bound is optimal in the sense there are TU-games for which the number of blocks required to access the core is exactly n−1.

We study the set of allocation rules generated by component efficiency and weighted component fairness, a generalization of component fairness introduced by Herings et al. (2008). Firstly, if the underlying TU-game is superadditive, this set coincides with the core of a graph-restricted game...

This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than...

We replace the axiom of fairness used in the characterization of the Myerson value (Myerson, 1977) by fairness for neighbors in order to characterize the component-wise egalitarian solution. When a link is broken, fairness states that the two players incident to the link should be affected...

In this paper, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We introduce natural extensions of the average (rooted)-tree solution (see [Herings, P., van der Laan,...