Stochastic Models of Coalition Games for Spectrum Sharing in Large Scale Interference Channels

In this paper, we present a framework for analysis of self organized distributed coalition formation process for spectrum sharing in interference channel for large scale ad hoc networks. In this approach we define coalition clusters within the network where mutual interdependency between different clusters is characterized by the concept of spatial network correlation. Then by using stochastic models of the process we give up some details which are characteristic for coalition game theory in order to be able to include some additional parameters for network scaling. Applications of this model are: a) Estimation of average time to reach grand coalition and its variance σ_τ² through closed form equations. These parameters are important in designing the process in dynamic environment. b) Dimensioning the coalition cluster within the network c) Modelling the network spatial correlation characterizing mutual visibility of the interfering links. d) Modelling of the effect of the new link activation/inactivation on the coalition forming process. e) Modelling the effect of link mobility on the coalition forming process.