We study the existence problem of a zero point of a function defined on a finite set of elements of the integer lattice of the n-dimensional Euclidean space . It is assumed that the set is integrally convex, which implies that the convex hull of the set can be subdivided in simplices such that...

The Reverse Talmud rule for bankruptcy problems applies the Constrained Equal Awards rule (CEA rule) for ‘large’ amounts of the estate, while it applies the Constrained Equal Losses rule (CEL rule) for ‘small’ amounts of the estate. The CEA rule, respectively CEL rule, can be axiomatized...

A cooperative game with a permission structure describes a situation in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. In this paper we consider non-negative...

In a standard TU-game it is assumed that every subset of the player set N can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure of Aumann and Drèze (1974). They assumed that the player set...