A situation in which a finite set of players can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility. A solution for TU-games assigns to every TU-game a distribution of the payoffs that can be earned over the individual players. Two well-known...

In this paper shortest path games are considered. The transportation of a good in a network has costs and benefit too. The problem is to divide the profit of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of...

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.

A new model of TU game is introduced and studied. Here apart from the characteristic function, two additional functions are used: relations between the players and the probability of coalition formation. We suggest and study the sufficient properties of the probability function to transform it...

The principle of additivity states the sum of payoffs in two separate games should equal the payoff in the combination of both games. We show that the Shapley value is the only value that is additive for arbitrary games and that equally divides the payoff in games in which only the grand...

Lloyd S. Shapley introduced a set of axioms in 1953, now called the Shapley axioms, and showed that the axioms characterize a natural allocation among the players who are in grand coalition of a cooperative game. Recently, Stern and Tettenhorst showed that a cooperative game can be decomposed...

An individual bank can put the whole banking system at risk if its losses in response to shocks push losses for the system as a whole above a critical threshold. We determine the contribution of banks to this systemic risk using a generalisation of the Shapley value; a concept originating in...

We use the axiomatization of the position value for network situations in van den Nouweland and Slikker (2012) to define a position value for partition function form network situations by generalizing the axioms to the partition function form value function setting as studied in Navarro (2007)...

We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over the coalitional behavior of the outsiders, i.e., it...

Selfish, strategic players may benefit from cooperation, provided they reach agreement. It is therefore important to construct mechanisms that facilitate such cooperation, especially in the case of asymmetric private information. The two major issues are: (1) singling out a fair and efficient...