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The Impact of Social Ignorance on Weighted Congestion Games

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Abstract

We consider weighted linear congestion games, and investigate how social ignorance, namely lack of information about the presence of some players, affects the inefficiency of pure Nash equilibria (PNE) and the convergence rate of the ε-Nash dynamics. To this end, we adopt the model of graphical linear congestion games with weighted players, where the individual cost and the strategy selection of each player only depends on his neighboring players in the social graph. We show that such games admit a potential function, and thus a PNE. Next, we investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) of graphical linear congestion games with respect to the players’ total actual cost. Our main result is that the impact of social ignorance on the PoA and on the PoS is naturally quantified by the independence number α(G) of the social graph G. In particular, we show that the PoA grows roughly as α(G)(α(G)+2), which is essentially tight as long as α(G) does not exceed half the number of players, and that the PoS lies between α(G) and 2α(G). Moreover, we show that the ε-Nash dynamics reaches an α(G)(α(G)+2)-approximate configuration in polynomial time that does not directly depend on the social graph. For unweighted graphical linear games with symmetric strategies, we show that the ε-Nash dynamics reaches an ε-approximate PNE in polynomial time that exceeds the corresponding time for symmetric linear games by a factor at most as large as the number of players.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece

    Dimitris Fotakis

  2. Computer Science Department, Courant Institute, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Vasilis Gkatzelis

  3. Department of Information and Communication Systems Engineering, University of the Aegean, 83200, Samos, Greece

    Alexis C. Kaporis

  4. Research Academic Computer Technology Institute, N. Kazantzaki Str., University Campus, 26500, Patras, Greece

    Alexis C. Kaporis & Paul G. Spirakis

Authors
  1. Dimitris Fotakis
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  2. Vasilis Gkatzelis
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  3. Alexis C. Kaporis
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  4. Paul G. Spirakis
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Corresponding author

Correspondence to Dimitris Fotakis.

Additional information

This work was partially supported by an NTUA Basic Research Grant (PEBE 2009), NSF grant CCF0830516, Andreas Mentzelopoulos Scholarships for the University of Patras, and the ICT Programme of the EU, under contract no. ICT-2008-215270 (FRONTS). An extended abstract of this work appeared in the Proceedings of the 5th International Workshop on Internet and Network Economics (WINE 2009), Stefano Leonardi (ed.), Lecture Notes in Computer Science, vol. 5929, pp. 316–327. Springer, Berlin, 2009.

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Fotakis, D., Gkatzelis, V., Kaporis, A.C. et al. The Impact of Social Ignorance on Weighted Congestion Games. Theory Comput Syst 50, 559–578 (2012). https://doi.org/10.1007/s00224-011-9355-2

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