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Dynamic Network Congestion Games

Authors Nathalie Bertrand , Nicolas Markey , Suman Sadhukhan, Ocan Sankur

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Nathalie Bertrand
  • Univ Rennes, Inria, CNRS, IRISA, Rennes, France
Nicolas Markey
  • Univ Rennes, Inria, CNRS, IRISA, Rennes, France
Suman Sadhukhan
  • Univ Rennes, Inria, CNRS, IRISA, Rennes, France
Ocan Sankur
  • Univ Rennes, Inria, CNRS, IRISA, Rennes, France

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Nathalie Bertrand, Nicolas Markey, Suman Sadhukhan, and Ocan Sankur. Dynamic Network Congestion Games. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSTTCS.2020.40

Abstract

Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games (NCGs), the resources correspond to simple paths in a graph, e.g. representing routing options from a source to a target. In this paper, we introduce a variant of NCGs, referred to as dynamic NCGs: in this setting, players take transitions synchronously, they select their next transitions dynamically, and they are charged a cost that depends on the number of players simultaneously using the same transition. We study, from a complexity perspective, standard concepts of game theory in dynamic NCGs: social optima, Nash equilibria, and subgame perfect equilibria. Our contributions are the following: the existence of a strategy profile with social cost bounded by a constant is in PSPACE and NP-hard. (Pure) Nash equilibria always exist in dynamic NCGs; the existence of a Nash equilibrium with bounded cost can be decided in EXPSPACE, and computing a witnessing strategy profile can be done in doubly-exponential time. The existence of a subgame perfect equilibrium with bounded cost can be decided in 2EXPSPACE, and a witnessing strategy profile can be computed in triply-exponential time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Verification by model checking
Keywords
  • Congestion games
  • Nash equilibria
  • Subgame perfect equilibria
  • Complexity

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