Properties of epg under load-dependent travel times

Determine whether the Evacuation Planning Game (epg) continues to exhibit its key theoretical properties when edge travel times are load-dependent rather than constant; specifically, ascertain the existence of pure strategy Nash equilibria and derive whether bounds on the Price of Anarchy still hold under congestion-dependent delays.

Background

The paper introduces the Evacuation Planning Game (epg), in which agents choose both routes and departure times on an evacuation network, and proves (under the assumptions of constant edge travel times and confluent routes) the existence of pure strategy Nash equilibria and tight bounds on the Price of Anarchy across instances.

In the limitations section, the authors explicitly state that extending these results to settings with load-dependent, congestion-sensitive travel times remains unresolved, raising core questions about whether equilibrium existence and inefficiency bounds persist when travel times vary with traffic.

References

There are several questions regarding the Evacuation Planning Game (epg) that remain open. Some specific questions are: (i) In epg, we consider the travel time on each edge to be a constant. Do the properties of epg change if we consider load-dependent travel times (e.g. does pure strategy Nash equilibrium still exist, do the Price of Anarchy bounds still hold)?

— A Scalable Game-theoretic Approach to Urban Evacuation Routing and Scheduling  (2401.04371 - Islam et al., 2024) in Conclusion, Limitations, and Future Work (Section 6)