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The Strong Price of Anarchy of Linear Bottleneck Congestion Games

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Abstract

We study the inefficiency of equilibrium outcomes in Bottleneck Congestion games. These games model situations in which strategic players compete for a limited number of facilities. Each player allocates his weight to a (feasible) subset of the facilities with the goal to minimize the maximum (weight-dependent) latency that he experiences on any of these facilities. We analyze the (strong) Price of Anarchy of these games for a natural load balancing social cost objective, i.e., minimize the maximum latency of a facility. In our studies, we focus on Bottleneck Congestion games with linear latency functions. These games still constitute a rich class of games and generalize, for example, Load Balancing games with identical or uniformly related machines (with or without restricted assignments). We derive upper and (asymptotically) matching lower bounds on the (strong) Price of Anarchy of these games. We also derive more refined bounds for several special cases of these games, including the cases of identical player weights, identical latency functions and symmetric strategy sets. Further, we provide lower bounds on the Price of Anarchy for k-strong equilibria.

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Notes

  1. We use [k] to refer to the set \(\{1, \dots , k\}\) for some positive integer k.

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Acknowledgments

We thank two anonymous reviewers who helped us significantly in improving the presentation of this work.

Orestis Telelis acknowledges support by the research project “DDCOD” (PE6-213). The project is implemented within the framework of the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Union (European Social Fund – ESF) and the Greek State.

Bart de Keijzer acknowledges support by the EU FET project MULTIPLEX no. 317532, the ERC StG Project PAAI 259515, and the Google Research Award for Economics and Market Algorithms.

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Authors and Affiliations

  1. Web Algorithmics and Data Mining Group, Sapienza University of Rome. DIAG, 00185, Rome, Italy

    Bart de Keijzer

  2. Networks and Optimization Group, Centre for Mathematics and Computer Science (CWI), Science Park 123, 1098XG, Amsterdam, The Netherlands

    Guido Schäfer

  3. Department of Econometrics and Operations Research, VU University Amsterdam, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlands

    Guido Schäfer

  4. Department of Digital Systems, University of Piraeus, 18534, Piraeus, Greece

    Orestis Telelis

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  1. Bart de Keijzer
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  2. Guido Schäfer
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  3. Orestis Telelis
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Correspondence to Orestis Telelis.

Additional information

A preliminary version of this work appeared in [12].

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Keijzer, B.d., Schäfer, G. & Telelis, O. The Strong Price of Anarchy of Linear Bottleneck Congestion Games. Theory Comput Syst 57, 377–396 (2015). https://doi.org/10.1007/s00224-014-9598-9

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