Network formation models with costs for establishing links

In this paper we study endogenous formation of communication networks in situations where the economic possibilities of groups of players can be described by a cooperative game. We concentrate on the influence that the existence of costs for establishing communication links has on the communication networks that are formed. The starting points in this paper are two game-theoretic models of the formation of communication links that were studied in the literature fairly recently, the extensive-form model by Aumann and Myerson (1988) and the strategic-form model that was studied by Dutta, van den Nouweland and Tijs (1998). We follow their analyses as closely as possible and use an extension of the Myerson value to determine the payoffs to the players in communication situations when forming links is not costless. We find that for both models, the pattern of structures formed as costs increase depends on whether the underlying coalitional game is superadditive and/or convex.