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Some users of a communications network may have more information about traffic on the network than others do-and this fact may be secret. Such secret information would allow the possessor to tailor its own traffic to the traffic of others; this would help the secret information possessor or informed user and (might) harm other uninformed users. To quantitatively study the impact of secret information, we formulate a flow control game with incomplete information where users choose their flows in order to maximize their (expected) utilities given the distribution of the actions of others. In this environment, the natural baseline notion is Bayesian Nash Equilibrium (BNE); we establish the existence of BNE. Next, we assume that there is a user who knows the realized congestion created by other users, but that the presence of this informed user is not known by other uninformed users; thus, the informed user has secret information. For this environment, we define a new equilibrium concept: the Bayesian Nash Equilibrium with Secret Information (BNE-SI) and establish its existence. We establish rigorous estimates for the benefit (to the informed user) and harm (to the uninformed users) that result from secret information; both the benefit and the harm become smaller for large networks. Interestingly, simulations demonstrate that secret information may in fact benefit all users. Secret information may also harm uninformed users in particular scenarios. This analysis can be used as a starting point for securing communications networks, both from the network manager and the user's perspectives.