We propose a model for network optimization in a non-cooperative game setting with specific reference to the Internet connectivity. The model describes the decisions taken by an Autonomous System (AS) when joining the Internet. We first define a realistic model for the interconnection costs incurred; then we use this cost model to perform a game theoretic analysis of the decisions related to link creation and traffic routing, keeping into account the peering/transit dichotomy. The proposed model doesn't fall into the standard category of routing games, hence we devise new tools to solve it by exploiting specific properties of our game. We prove analytically the existence of multiple equilibria 219