Public congestion network situations and related games

Abstract

This article analyses congestion in network situations from a cooperative game theoretic perspective. In network situations, players have to connect themselves to a source. As we consider publicly available networks, any group of players is allowed to use the entire network to establish their connections. We deal with the problem of finding an optimal network and discuss the associated cost allocation problem. For the latter, we introduce two different transferable utility cost games. For concave cost functions, we use the direct cost game, in which coalition costs are based on what a coalition can do in the absence of other players. This article, 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 equal treatment 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. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010