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Routing Games over Time with FIFO Policy

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Web and Internet Economics (WINE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10660))

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Abstract

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a first-in-first-out queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue’s head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.

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Notes

  1. 1.

    Static routing games were a crucial testbed for the Price of Anarchy, a concept that bounds a game’s loss of efficiency due to selfish behaviors.

  2. 2.

    [WHK14, Appendix B.1, Fig. B.11] contains a similar result.

  3. 3.

    A close Dijkstra-style algorithm for local priorities lies in [HPSVK16, Proposition 2.2].

  4. 4.

    [WHK14, Sect. 7] claims that one can derive NP-hardness for sum-objectives.

  5. 5.

    A walk is an alternating sequence of vertices and edges, consistent with the given (di)graph, and that allows repetitions and infiniteness.

  6. 6.

    A degenerate agent only has one strategy, but can still incur and cause externalities.

  7. 7.

    An L-reduction is a poly.-time reduction in NPO, which conserves approximations.

  8. 8.

    Class \(\varSigma _2^P\) are the problems that nest a coNP problem inside an NP problem.

    Only very small sizes (\({\lessapprox }10\)) of such problems can usually be practically addressed.

  9. 9.

    For two variables x, y, Landau notation \(f(x,y)\in \varOmega (g(x,y))\) is defined as:

    \(\exists K\in \mathbb {R}_{>0},~\exists n_0\in \mathbb {N}_{\ge 0},~\forall x,y\ge n_0,~f(x,y)\ge Kg(x,y)\).

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Acknowledgments

I am grateful to the anonymous reviewers for their work. This work was supported by grant KAKENHI 15H01703.

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Authors and Affiliations

  1. Takayuki Ito Laboratory, Nagoya Institute of Technology, Nagoya, Japan

    Anisse Ismaili

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  1. Anisse Ismaili
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Correspondence to Anisse Ismaili .

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  1. Microsoft Research, Redmond, Washington, USA

    Nikhil R. Devanur

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Ismaili, A. (2017). Routing Games over Time with FIFO Policy. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_19

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  • DOI: https://doi.org/10.1007/978-3-319-71924-5_19

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