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On Network Congestion Reduction Using Public Signals Under Boundedly Rational User Equilibria (Full Version)

Olivier Massicot, Cédric Langbort

TL;DR

It is shown 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.

Abstract

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.

On Network Congestion Reduction Using Public Signals Under Boundedly Rational User Equilibria (Full Version)

TL;DR

It is shown 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.

Abstract

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.
Paper Structure (17 sections, 54 equations, 4 figures)

This paper contains 17 sections, 54 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Formal model
  3. Road networks and User Equilibria
  4. Boundedly Rational User Equilibria
  5. Welfare effect of bounded rationality
  6. Price of anarchy
  7. Average excess time due to bounded rationality
  8. Unboundedness of the inefficiency factor
  9. Information provision for bounded rationality
  10. Stochastic network
  11. Information design
  12. Designing information using UE as a proxy
  13. Designing information for large $\epsilon$
  14. Information revealed may increase with $\epsilon$
  15. Information revealed may be non-monotonic in $\epsilon$
  16. ...and 2 more sections

Figures (4)

  • Figure 1: A Wheatstone network, with unit demand crossing from the left to the right.
  • Figure 2: A chain of Wheatstone networks identical to those of Figure \ref{['fig:wheatstone']}.
  • Figure 3: A stochastic network for which information revealed increases with $\epsilon$, yet $\epsilon_0$-minimizer agents are worse off if the central planner believes $\epsilon\geq\epsilon_0$.
  • Figure 4: A stochastic network for which no monotonic (in $\epsilon$) sequence of public signals exist, $\omega\in\{0,1\}$.