A Game Theoretic Model for AS Topology Formation with the Scale-Free Property

Recent studies investigating the Internet topology reported that inter Autonomous System (AS) topology exhibits a power-law degree distribution which is known as the scale-free property. Although there are many models to generate scale-free topologies, no game theoretic approaches have been proposed yet. In this paper, we propose the new dynamic game theoretic model for the AS level Internet topology formation. Through numerical simulations, we show our process tends to give emergence of the topologies which have the scale-free property especially in the case of large decay parameters and large random link costs. The significance of our study is summarized as following three topics. Firstly, we show that scale-free topologies can also emerge from the game theoretic model. Secondly, we propose the new dynamic process of the network formation game for modeling a process of AS topology formation, and show that our model is appropriate in the micro and macro senses. In the micro sense, our topology formation process is appropriate because this represents competitive and distributed situation observed in the real AS level Internet topology formation process. In the macro sense, some of statistical properties of emergent topologies from our process are similar to those of which also observed in the real AS level Internet topology. Finally, we demonstrate the numerical simulations of our process which is deterministic variation of dynamic process of network formation game with transfers. This is also the new result in the field of the game theory. key words: complex networks, strategic network formation, Internet topology, scale-free networks, game theory