Abstract
We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and in contrast to these notions is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games.
We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players’ individual interests and the impact of their decisions on the society as a whole. Our analysis reveals that the selfishness level often provides more refined insights into the game than other measures of inefficiency, such as the price of stability or the price of anarchy.
A full version with all proofs is available at the authors’ homepages.
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
Jehle, G., Reny, P.: Advanced Microeconomic Theory, 3rd edn. Addison Wesley, New York (2011)
Koutsoupias, E., Papadimitriou, C.H.: Worst case equilibria. In: Annual IEEE Symposium on Theoretical Aspects of Computer Science, pp. 404–413 (1999)
Schulz, A.S., Moses, N.E.S.: On the performance of user equilibria in traffic networks. In: SODA, pp. 86–87 (2003)
Axelrod, R.: The Evolution of Cooperation. Basic Books (1984)
Ledyard, J.O.: 2. The Handbook of Experimental Economics. In: Public Goods: A Survey of Experimental Research, pp. 111–194. Princeton University Press (1995)
Marco, G.D., Morgan, J.: Slightly altruistic equilibria in normal form games. Working paper No 185, Center for Studies in Economics and Finance, University of Salerno, Italy (2007), http://www.csef.it/WP/wp185.pdf
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: Proc. 10th ACM Conference on Electronic Commerce, pp. 140–149 (2008)
Elias, J., Martignon, F., Avrachenkov, K., Neglia, G.: Socially-aware network design games. In: Proc. INFOCOM 2010, pp. 41–45 (2010)
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)
Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proc. 41st Annual ACM Symposium on Theory of Computing, pp. 513–522 (2009)
Beckmann, M., McGuire, B., Winsten, C.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)
Sharma, Y., Williamson, D.P.: Stackelberg thresholds in network routing games or the value of altruism. Games and Economic Behavior 67(1), 174–190 (2009)
Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behaviour 14, 124–143 (1996)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory (2), 65–67 (1973)
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: Proc. 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 295–304 (2004)
Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. 37th Annual ACM Symposium on Theory of Computing (2005)
Awerbuch, B., Azar, Y., Epstein, A.: Large the price of routing unsplittable flow. In: Proc. 37th Annual ACM Symposium on Theory of Computing, pp. 57–66 (2005)
Osborne, M.J.: An Introduction to Game Theory. Oxford University Press, Oxford (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Apt, K.R., Schäfer, G. (2012). Selfishness Level of Strategic Games. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-33996-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33995-0
Online ISBN: 978-3-642-33996-7
eBook Packages: Computer ScienceComputer Science (R0)