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Performance of One-Round Walks in Linear Congestion Games

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Abstract

We investigate the approximation ratio of the solutions achieved after a one-round walk in linear congestion games. We consider the social functions Sum, defined as the sum of the players’ costs, and Max, defined as the maximum cost per player, as a measure of the quality of a given solution. For the social function Sum and one-round walks starting from the empty strategy profile, we close the gap between the upper bound of \(2+\sqrt{5}\approx 4.24\) given in Christodoulou et al. (Proceedings of the 23rd International Symposium on Theoretical Aspects of Computer Science (STACS), LNCS, vol. 3884, pp. 349–360, Springer, Berlin, 2006) and the lower bound of 4 derived in Caragiannis et al. (Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP), LNCS, vol. 4051, pp. 311–322, Springer, Berlin, 2006) by providing a matching lower bound whose construction and analysis require non-trivial arguments. For the social function Max, for which, to the best of our knowledge, no results were known prior to this work, we show an approximation ratio of \(\Theta(\sqrt[4]{n^{3}})\) (resp. \(\Theta(n\sqrt{n})\)), where n is the number of players, for one-round walks starting from the empty (resp. an arbitrary) strategy profile.

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Authors and Affiliations

  1. Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy

    Vittorio Bilò

  2. School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore, Singapore

    Angelo Fanelli

  3. Dipartimento di Informatica, Università di L’Aquila Via Vetoio, Loc. Coppito, 67100, L’Aquila, Italy

    Michele Flammini

  4. Dipartimento di Scienze, Università di Chieti-Pescara, Viale Pindaro 42, 65127, Pescara, Italy

    Luca Moscardelli

Authors
  1. Vittorio Bilò
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  2. Angelo Fanelli
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  3. Michele Flammini
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  4. Luca Moscardelli
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Corresponding author

Correspondence to Vittorio Bilò.

Additional information

This work was partially supported by the PRIN 2008 research project COGENT (COmputational and GamE-theoretic aspects of uncoordinated NeTworks), funded by the Italian Ministry of University and Research, and by the grant NRF-RF2009-08 “Algorithmic aspects of coalitional games”.

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Bilò, V., Fanelli, A., Flammini, M. et al. Performance of One-Round Walks in Linear Congestion Games. Theory Comput Syst 49, 24–45 (2011). https://doi.org/10.1007/s00224-010-9309-0

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