Congestion Network Problems and Related Games

This paper analyzes network problems with congestion effects from a cooperative game theoretic perspective.It is shown that for network problems with convex congestion costs, the corresponding games have a non-empty core.If congestion costs are concave, then the corresponding game has not necessarily core elements, but it is derived that, contrary to the convex congestion situation, there always exist optimal tree networks.Extensions of these results to a class of relaxed network problems and associated games are derived.

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

Cost allocation in connection and conflict problems on networks: a cooperative game theoretic approach

This thesis examines settings where multiple decision makers with conflicting interests benefit from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in joint single-source shortest path problems and joint weighted minimum colouring problems. The primary focus of the thesis are problems where each agent corresponds to a vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the shortest paths from the supplier to all other vertices in the graph. The optimal solution is a shortest path tree of the graph and the aim is to allocate the cost of this shortest path tree amongst the agents. The thesis defines shortest path tree problems, proposes allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core allocations for shortest path tree games are introduced and polyhedral properties of the core are studied. Moreover, computational results on finding the core and the nucleolus of shortest path tree games for the application of cost allocation in Wireless Multihop Networks are presented. The secondary focus of the thesis are problems where each agent is interested in having access to a number of facilities but can be in conflict with other agents. If two agents are in conflict, then they should have access to disjoint sets of facilities. The aim is to allocate the cost of the minimum number of facilities required by the agents amongst them. The thesis models these cost allocation problems as a class of cooperative games called weighted minimum colouring games, and characterises total balancedness and submodularity of this class of games using the properties of the underlying graph

Modelling interactive behaviour, and solution concepts

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Production externalities : cooperative and non-cooperative approaches

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Modelling interactive behaviour, and solution concepts.

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.