Protocols for data transmission over a TCP-like computer network should not only lead to efficient network utilization but also be fair to different users. Current networks accomplish these goals by some form of end-to-end congestion control. However, existing protocols assume somewhat altruistic behavior from hosts, and Karp et al.  have initiated a study of whether or not the host's optimum strategy is altruistic. We carry this exploration further by developing an efficient randomized algorithm for bandwidth utilization in their model. The competitive ratio of this algorithm is optimal up to a constant factor. Karp et al. had earlier studied the deterministic case and left open the randomized case. What may be of some interest is that our algorithm is essentially the classical MIMD (multiplicative increase, multiplicative decrease) strategy, which is very aggressive and non-altruistic.