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The Internet uses a model in which Autonomous Systems (AS) peer bilaterally with each other, resulting in a cascaded connectivity model: the end-to-end service that an end-user sees is the result of this cascade of bilateral traffic agreements. As a result, the routing decisions at each AS beyond the next hop are implicitly delegated, so an AS has limited control over the remaining path. While this may be considered a key feature of the Internet (e.g., helps scalability), the impact of this cascading model on the structure of the Internet is not yet well understood. In this paper, we analyze this cascaded model using concepts of game theory. Although our model cannot capture the full complexity of the real Internet - we actually aim at simplicity and try to only isolate the cascading effect -, our results suggest that cascading bilateral agreements brings order to an arbitrary graph. In particular, it brings forward some well-known properties of the Internet topology, such as the current AS hierarchy and common peering models. Finally, we compare our results with topological and routing data, obtained from CAIDA, looking for experimental evidence of our results, while further exploring the insight obtained from our model.