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Non-Blind Strategies in Timed Network Congestion Games
Computer Science and Game Theory · Submitted 4 Jul 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.05 | 0.02 | asserted 0.99 |
| s1 | Network congestion games have been extensively studied over the last 40 years, while their extension with timing constraints were considered more recently. | background 0.99 | 0.04 | 0.02 | asserted 1.00 |
| s2 | 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. | background 0.85 | 0.05 | 0.03 | asserted 1.00 |
| s3 | We extend the recent results of [Bertrand et al., Dynamic network congestion games. | contribution 0.98 | 0.71 | 0.04 | asserted 0.77 |
| s4 | FSTTCS'20] to timed network congestion games, in which the availability of the edges depend on (discrete) time. | contribution 0.87 | 0.56 | 0.05 | asserted 0.88 |
| s5 | 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. | result 0.99 | 0.95 | 0.68 | asserted 1.00 |
| s6 | The social optimum can be computed in polynomial space if all players have the same source and target. | result 1.00 | 0.88 | 0.11 | asserted 1.00 |
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The paper
Original 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.
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