Recently, the scheme of parallel downloading has been proposed as a novel approach to expedite the reception of a large file from the Internet. Experiments with a single client have shown that the client can improve its performance significantly by using the scheme. Simulations and experiments with multiple clients using the scheme have been conducted in [8, 9] to investigate the impact that this technique might have on the network if it is widely adopted. Contrast to the methodology used in [8, 9], we formulate parallel downloading as a non-cooperative game. Within this framework, we present a characterization of the traffic configuration at Nash equilibrium in a general network, and analyze its properties in a specific network. We also establish the dynamic convergence to equilibrium from an initial non-equilibrium state for a specific network. Finally, we investigate the efficiency of Nash equilibrium from the point of view of the clients and the system respectively, i.e., downloading latencies perceived by individual clients and total latencies over all connections. We find that although the traffic configuration at Nash equilibrium is optimal from the point of view of the clients, it may be bad from the point of view of the system.