We study the interactions among self-interested users of network resources in the context of congestion control and routing protocols in computer networks.

In the context of congestion control, we propose a game-theoretic study of the selfish behavior of TCP users when they are allowed to use multiple concurrent TCP connections so as to maximize their goodputs (or other utility function). We refer to this as the TCP connection game. We demonstrate the existence and uniqueness of Nash equilibrium in several variants of this game. We also generalize this game to model peer-to-peer unstructured file sharing networks. The bad news is that the loss of efficiency (the price of anarchy) at the Nash Equilibrium can be arbitrarily large if users have no resource limitations and are not socially responsible. The good news is that, if either of these two factors is considered, the loss of efficiency is bounded.

We then study the interaction between overlay routing controller and underlay native network routing controller using two approaches. In the first approach, we formulate this interaction as a two-player game, in which the overlay network seeks to minimize the delay of its overlay traffic while the underlay network seeks to minimize the network cost as a whole. We show that the selfish behavior of the overlay network can cause huge cost increase and oscillation in the entire network. Even worse, we have identified cases in which the overlay network's cost increases as the game proceeds even though the overlay plays optimally in response to the underlay network's routing at each round. To solve this conflict, we propose that the overlay network plays as a leader in a Stackelberg game. In the second approach, we investigate the ability of an overlay network to compensate for "careless" routing in the native network layer, i.e., for network-layer routes not optimized for the performance of application overlays. In particular, we investigate the extent to which overlay-over-careless-underlay can achieve performance close to that attainable when underlay routing is performed in an optimal ("careful") manner. We find that the overlay network can compensate for careless underlay routing only when the sub-graph formed by the underlay network's routes is rich, which can be collectively characterized by three graph-theoretic metrics. This result suggests that ISPs can simplify underlay network management by relegating responsibility for performance to application overlays.