In this paper, we deal with a multicriteria competitive Markov decision process. In the decision process there are two decision makers with a competitive behaviour, so they are usually called players. Their rewards are coupled because depend on the actions chosen by both players in each state of...

In this paper we consider a new class of continuous location problems where the “distances” are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where...

Cost spanning tree problems concern the construction of a tree which provides a connection with the source for every node of the network. In this paper, we address cost sharing problems associated to these situations when the agents located at the nodes act in a non-cooperative way. A class of...

Ausgehend von kontinuierlichen 1-Standortproblemen wird in diesem Paper eine neue Klasse von kostenbasierten TU-Spielen eingeführt. Es werden einige hinreichende Bedingungen präsentiert unter denen ein Spiel in dieser Klasse einen nicht-leeren Kern hat. Weiterhin werden Zuordnungsregeln für...

In this paper we consider the general question in the field of mathematics of whether some properties or algorithms that hold in finite dimension spaces also hold in function spaces. We answer this question concerning the very well-known Weiszfeld algorithm for the Weber problem. In order to do...

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow...

When dealing with location problems we are usually given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing...

In this paper we analyze a new location problem which is a generalization of the well-known single facility location model. This extension consists of introducing a general objective function and replacing fixed locations by trajectories. We prove that the problem is well-stated and solvable. A...