How (information theoretically) optimal are distributed decisions?

¿If we know more, we can achieve more.¿ This adage also applies to networks, where more information about the network state translates into higher sum-rates. In this paper, we formalize this increase of sum-rate with increased knowledge of network. The knowledge of network is measured in terms of the number of hops of information about the network while the sum-rate is normalized by the maximum sum-rate that can be achieved with complete information. As the knowledge about the network increase, the achievable normalized sum-rate also increases. The best normalized sum-rate is called normalized sum-capacity. In this paper, we characterize the increase of normalized sum-capacity with the hops of information about the network for many classes of deterministic interference networks for the cases of one and two-hops of instantaneous channel information.