Game-theoretic formulations of the resource allocation problem have existed for a while. However, the issue of perfect knowledge continues to be a significant hurdle on the path to realistic implementations. In this paper, the notion of playing bandwidth allocation games is investigated under imperfect information. Specifically we look at the case of connection oriented networks regulated by resource pricing. We devise a distributed adaptive control strategy based on dynamic estimation in order to cope up with the uncertainty of noise and delay. Simulation results illustrate the scalability and accuracy of the algorithms under multiple scenarios. Potential applications include teletraffic and optical networks, as well as ad hoc wireless networks, enabling users to partition bandwidth without the need of a centralized synchronizing entity.