Nicolas Markey

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.

@inproceedings{formats2022-GMS,
  author =              {Goeminne, Aline and Markey, Nicolas and Sankur,
                         Ocan},
  title =               {Non-Blind Strategies in Timed Network Congestion
                         Games},
  editor =              {Bogomolov, Sergiy and Parker, David},
  booktitle =           {{P}roceedings of the 20th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'22)},
  acronym =             {{FORMATS}'22},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {13465},
  pages =               {183-199},
  year =                {2022},
  month =               sep,
  doi =                 {10.1007/978-3-031-15839-1_11},
  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. \par 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~\textit{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.},
}