The benefit of ignorance in routing traffic through a congestible network

Networks with self-interested users, such as traffic networks, are highly susceptible to congestion on the most efficient routes. This congestion often leads to a suboptimal traffic distribution which increases the average commute time, and this suboptimality is quantified by the so-called ``price of anarchy'' (POA). Previous work considered the POA for a random network of congestible and incongestible links and showed that the POA is maximal when the congestible link fraction is at the percolation threshold. Here we consider what happens to the network performance within this same model when users have incomplete knowledge of the cost of each link. We propose a new measure, the ``price of ignorance'', and we show that ignorance is in fact universally beneficial at a low level. Surprisingly, a certain optimal level of ignorance causes the Nash equilibrium for the network usage to coincide with the optimal behavior. We present numerical results which we explain with analytical arguments.