We present a game-theoretic model that captures many of the intricacies of interdomain routing in today's internet, in this model, the strategic agents are source nodes located on a network, who aim to send traffic to a unique destination node. The interaction between the agents is dynamic and complex - asynchronous, sequential, and based on partial information. Best-reply dynamics in this model capture crucial aspects of the interdomain routing protocol de facto, namely the Border Gateway Protocol (BGP). We study complexity and incentive-related issues in this model. Our main results are showing that in realistic and well-studied settings, BGP is incentive-compatible, i.e., not only does myopic behaviour of all players converge to a "stable" routing outcome, but no player has motivation to unilaterally deviate from the protocol. Moreover, we show that even coalitions of players of any size cannot improve their routing outcomes by collaborating. Unlike the vast majority of works in mechanism design, our results do not require any monetary transfers (to or by the agents).