Non-Blind Strategies in Timed Network Congestion Games

TL;DR

This paper extends the study of network congestion games to include timing constraints, analyzing the complexity of computing equilibria and social optima in timed scenarios.

Contribution

It introduces the concept of timed network congestion games and proves complexity results for computing Nash equilibria and social optima in these settings.

Findings

Computing constrained Nash equilibria is exponential space-hard.

Social optimum can be computed in polynomial space when players share source and target.

Results extend previous work to include discrete time constraints in congestion games.

Abstract

Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using the same link. Network congestion games have been extensively studied over the last 40 years, while their extension with timing constraints were considered more recently. Most of the results on network congestion games consider blind strategies: they are static, and do not adapt to the strategies selected by the other players. We extend the recent results of [Bertrand et al., Dynamic network congestion games. FSTTCS'20] to timed network congestion games, in which the availability of the edges depend on (discrete) time. We prove that computing Nash equilibria satisfying some constraint on the total cost (and in particular, computing the best and worst Nash equilibria), and computing the social optimum, can be achieved in exponential space. The social optimum can be computed in polynomial space if all players have the same source and target.