Finite Coverings by Cones

This paper considers analogues of statements concerning compactness and finite coverings, in which the roles of spheres are replaced by cones. Furthermore, one of the finite covering results provides an application in Multi-Objective Programming; infinite sets of alternatives are reduced to finite sets.cones;finite coverings

Public Congestion Network Situations, and Related Games

This paper analyzes congestion effects on network situations from a cooperative game theoretic perspective. In network situations players have to connect themselves to a source. Since we consider publicly available networks any group of players is allowed to use the entire network to establish their connection. We deal with the problem of finding an optimal network, the main focus of this paper is however to discuss the arising cost allocation problem. For this we introduce two different transferable utility cost games. For concave cost functions we use the direct cost game, where coalition costs are based on what a coalition can do in absence of other players. This paper however mainly discusses network situations with convex cost functions, which are analyzed by the use of the marginal cost game. In this game the cost of a coalition is defined as the additional cost it induces when it joins the complementary group of players. We prove that this game is concave. Furthermore, we define a cost allocation by means of three egalitarian principles, and show that this allocation is an element of the core of the marginal cost game. These results are extended to a class of continuous network situations and associated games.Congestion;network situations;cooperative games;public

Convex Congestion Network Problems

This paper analyzes convex congestion network problems.It is shown that for network problems with convex congestion costs, an algorithm based on a shortest path algorithm, can be used to find an optimal network for any coalition. Furthermore an easy way of determining if a given network is optimal is provided.game theory;cooperative games;algorithm

Informationally Robust Equlibria

Informationally Robust Equilibria (IRE) are introduced in Robson (1994) as a refinement of Nash equilibria for e.g. bimatrix games, i.e. mixed extensions of two person finite games.Similar to the concept of perfect equilibria, basically the idea is that an IRE is a limit of some sequence of equilibria of perturbed games.Here, the perturbation has to do with the hypothetical possibility that the action of one the players is revealed to his fellow player before the fellow player has to decide on his own action.Whereas Robson models these perturbations in extensive form and uses subgame perfection to solve these games, we model the perturbations in strategic form, thus remaining in the class of bimatrix games. Moreover, within the perturbations we impose two possible types of tie breaking rules, which leads to the notions optimistic and pessimistic IRE.The paper provides motivation on IRE and its definition.Several properties will be discussed.In particular, we have that IRE is a strict concept, and that IRE components are faces of Nash components.Specific results from potential gamesnash equilibria;game theory;information

Processing Games with Shared Interest

A generalization of processing problems with restricted capacities is introduced.In a processing problem there is a finite set of jobs, each requiring a specific amount of effort to be completed, whose costs depend linearly on their completion times.The new aspect is that players have interest in all jobs. The corresponding cooperative game of this generalization is proved to be totally balanced.Processing games;scheduling;core allocation

Finite Coverings by Cones

This paper considers analogues of statements concerning compactness and finite coverings, in which the roles of spheres are replaced by cones. Furthermore, one of the finite covering results provides an application in Multi-Objective Programming; infinite sets of alternatives are reduced to finite sets.

Public Congestion Network Situations, and Related Games

This paper analyzes congestion effects on network situations from a cooperative game theoretic perspective. In network situations players have to connect themselves to a source. Since we consider publicly available networks any group of players is allowed to use the entire network to establish their connection. We deal with the problem of finding an optimal network, the main focus of this paper is however to discuss the arising cost allocation problem. For this we introduce two different transferable utility cost games. For concave cost functions we use the direct cost game, where coalition costs are based on what a coalition can do in absence of other players. This paper however mainly discusses network situations with convex cost functions, which are analyzed by the use of the marginal cost game. In this game the cost of a coalition is defined as the additional cost it induces when it joins the complementary group of players. We prove that this game is concave. Furthermore, we define a cost allocation by means of three egalitarian principles, and show that this allocation is an element of the core of the marginal cost game. These results are extended to a class of continuous network situations and associated games.