In this paper we describe the extreme points of two closely related polytopes that are assigned to a digraph. The first polytope is the set of all sharing vectors (elements from the unit simplex) such that each node gets at least as much as each of its successors. The second one is the set of...

Many economic and social situations can be represented by a digraph. Both axiomatic and iterativemethods to determine the strength or power of all the nodes in a digraph have been proposed inthe literature. We propose a new method, where the power of a node is determined by both thenumber of its...

Network shares and retail prices are not symmetric in the telecommunications market with multiple bottlenecks which give rise to new questions of access fee regulation. In this paper we consider a model with two types of asymmetry arising from different entry timing, i.e. a larger reputation for...

Some 2000 years ago, the average annual distance a person would normally travel, was approximately 500 km. The action radius of most people remained rather stable, but it rose gradually after the industrial revolution to some 1820 km (by car, bus, railway or aircraft) in the year 1960. Then, a...