Modeling the Dynamics of Coalition Formation Games for Cooperative Spectrum Sharing in an Interference Channel

Although establishing cooperation in a wireless network is a dynamic process, most game theoretic coalition formation models proposed in the literature are static. We analyze a dynamic coalition formation game based on a Markovian model for the spectrum sharing problem in an interference channel. Our model is dynamic in the sense that distributed transmitter/receiver pairs, with partial channel knowledge, reach stable coalition structures (CSs) through a time-evolving sequence of steps. Depending on an interference environment, we show that the game process either converges to the absorbing state of the grand coalition or to the absorbing state of internal and external stability. We also show that, due to myopic links, it is possible that the core of the game is nonempty, but links cannot form the grand coalition to utilize the core rate allocations. We then formulate a condition for the formation of the stable grand coalition. Using simulation we show that coalition formation yields significant gains in terms of average rates per link for different network sizes. We also show average maximum coalition sizes for different distances between the transmitters and their own receivers. Finally, we analyze the mean and variance of the time for the game to reach the stable coalition structures.