  Boundedly Rational User Equilibria (BRUE) capture situations where all agents
on a transportation network are electing the fastest option up to some time
indifference, and serve as a relaxation of User Equilibria (UE), where each
agent exactly minimizes their travel time. We study how the social cost under
BRUE departs from that of UE in the context of static demand and stochastic
costs, along with the implications of BRUE on the optimal signaling scheme of a
benevolent central planner. We show that the average excess time is sublinear
in the maximum time indifference of the agents, though such aggregate may hide
disparity between populations and the sublinearity constant depends on the
topology of the network. Regarding the design of public signals, even though in
the limit where agents are totally indifferent, it is optimal to not reveal any
information, there is in general no trend in how much information is optimally
disclosed to agents. What is more, an increase in information disclosed may
either harm or benefit agents as a whole.
