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...

We consider the problem of sharing water among agents located along a river. Each agent's benefit depends on the amount of water consumed. An allocation of water is efficient when it maximizes total benefits. To sustain an efficient water allocation the agents can compensate each other by...

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...

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...

In this note we provide a strategic implementation of the Average Tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This...