Abstract
We study the issues of existence and inefficiency of pure Nash equilibria in linear congestion games with altruistic social context, in the spirit of the model recently proposed by de Keijzer et al. [14]. In such a framework, given a real matrix Γ = (γ ij ) specifying a particular social context, each player i aims at optimizing a linear combination of the payoffs of all the players in the game, where, for each player j, the multiplicative coefficient is given by the value γ ij . We give a broad characterization of the social contexts for which pure Nash equilibria are always guaranteed to exist and provide tight or almost tight bounds on their prices of anarchy and stability. In some of the considered cases, our achievements either improve or extend results previously known in the literature.
This work was partially supported by the PRIN 2010–2011 research project ARS TechnoMedia: “Algorithmics for Social Technological Networks” funded by the Italian Ministry of University.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact Price of Anarchy for Polynomial Congestion Games. SIAM Journal on Computing 40(5), 1211–1233 (2011)
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The Price of Stability for Network Design with Fair Cost Allocation. SIAM Journal on Computing 38(4), 1602–1623 (2008)
Ashlagi, I., Krysta, P., Tennenholtz, M.: Social Context Games. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 675–683. Springer, Heidelberg (2008)
Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proceedings of STOC 2005, pp. 57–66. ACM Press (2005)
Bilò, V.: A Unifying Tool for Bounding the Quality of Non-cooperative Solutions in Weighted Congestion Games. In: Erlebach, T., Persiano, G. (eds.) WAOA 2012. LNCS, vol. 7846, pp. 215–228. Springer, Heidelberg (2013)
Bilò, V., Celi, A., Flammini, M., Gallotti, V.: Social Context Congestion Games. Theoretical Computer Science 514, 21–35 (2013)
Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight Bounds for Selfish and Greedy Load Balancing. Algorithmica 61(3), 606–637 (2011)
Caragiannis, I., Kaklamanis, C., Kanellopoulos, P., Kyropoulou, M., Papaioannou, E.: The Impact of Altruism on the Efficiency of Atomic Congestion Games. In: Wirsing, M., Hofmann, M., Rauschmayer, A. (eds.) TGC 2010, LNCS, vol. 6084, pp. 172–188. Springer, Heidelberg (2010)
Chen, P.-A., de Keijzer, B., Kempe, D., Schäfer, G.: The Robust Price of Anarchy of Altruistic Games. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) WINE 2011. LNCS, vol. 7090, pp. 383–390. Springer, Heidelberg (2011)
Chen, P.A., Kempe, D.: Altruism, Selfishness and Spite in Traffic Routing. In: Proceedings of EC 2008, pp. 140–149. ACM Press (2008)
Christodoulou, G., Gairing, M.: Price of Stability in Polynomial Congestion Games. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 496–507. Springer, Heidelberg (2013)
Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proceedings of STOC 2005, pp. 67–73. ACM Press (2005)
Christodoulou, G., Koutsoupias, E.: On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005)
Anagnostopoulos, A., Becchetti, L., de Keijzer, B., Schäfer, G.: Inefficiency of Games with Social Context. In: Vöcking, B. (ed.) SAGT 2013. LNCS, vol. 8146, pp. 219–230. Springer, Heidelberg (2013)
Fotakis, D., Kontogiannis, S., Spirakis, P.G.: Atomic Congestion Games among Coalitions. ACM Transactions on Algorithms 4(4) (2008)
Hoefer, M., Skopalik, A.: Altruism in Atomic Congestion Games. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 179–189. Springer, Heidelberg (2009)
Hoefer, M., Skopalik, A.: Social Context in Potential Games. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 364–377. Springer, Heidelberg (2012)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A New Model for Selfish Routing. Theoretical Computer Science 406(2), 187–206 (2008)
Rahn, M., Schäfer, G.: Bounding the Inefficiency of Altruism through Social Contribution Games. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 391–404. Springer, Heidelberg (2013)
Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. International Journal of Game Theory 2, 65–67 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bilò, V. (2014). On Linear Congestion Games with Altruistic Social Context. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_47
Download citation
DOI: https://doi.org/10.1007/978-3-319-08783-2_47
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08782-5
Online ISBN: 978-3-319-08783-2
eBook Packages: Computer ScienceComputer Science (R0)