WINE 2015: Web and Internet Economics pp 258-271

# The Curse of Sequentiality in Routing Games

• José Correa
• Jasper de Jong
• Bart de Keijzer
• Marc Uetz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)

## Abstract

In the “The curse of simultaneity”, Paes Leme et al. show that there are interesting classes of games for which sequential decision making and corresponding subgame perfect equilibria avoid worst case Nash equilibria, resulting in substantial improvements for the price of anarchy. This is called the sequential price of anarchy. A handful of papers have lately analysed it for various problems, yet one of the most interesting open problems was to pin down its value for linear atomic routing (also: network congestion) games, where the price of anarchy equals 5/2. The main contribution of this paper is the surprising result that the sequential price of anarchy is unbounded even for linear symmetric routing games, thereby showing that sequentiality can be arbitrarily worse than simultaneity for this class of games. Complementing this result we solve an open problem in the area by establishing that the (regular) price of anarchy for linear symmetric routing games equals 5/2. Additionally, we prove that in these games, even with two players, computing the outcome of a subgame perfect equilibrium is $$\mathsf {NP}$$-hard.

## Notes

### Acknowledgments

We thank Mathieu Faure for stimulating discussions and particularly for pointing out a precursor of the instance depicted in Fig. 2. We thank Marco Scarsini and Victor Verdugo for discussions on the price of anarchy of the symmetric atomic network game. We thank the reviewers for some helpful comments. We also thank Éva Tardos for allowing us to (partially) recycle their paper title from [14].

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## Authors and Affiliations

• José Correa
• 1
• Jasper de Jong
• 2
• Bart de Keijzer
• 3
• Marc Uetz
• 2