Selfishness Level of Strategic Games
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.
KeywordsTransportation Nash Rium Toll
Unable to display preview. Download preview PDF.
- 1.Jehle, G., Reny, P.: Advanced Microeconomic Theory, 3rd edn. Addison Wesley, New York (2011)Google Scholar
- 2.Koutsoupias, E., Papadimitriou, C.H.: Worst case equilibria. In: Annual IEEE Symposium on Theoretical Aspects of Computer Science, pp. 404–413 (1999)Google Scholar
- 3.Schulz, A.S., Moses, N.E.S.: On the performance of user equilibria in traffic networks. In: SODA, pp. 86–87 (2003)Google Scholar
- 4.Axelrod, R.: The Evolution of Cooperation. Basic Books (1984)Google Scholar
- 5.Ledyard, J.O.: 2. The Handbook of Experimental Economics. In: Public Goods: A Survey of Experimental Research, pp. 111–194. Princeton University Press (1995)Google Scholar
- 6.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
- 9.Chen, P.A., Kempe, D.: Altruism, selfishness, and spite in traffic routing. In: Proc. 10th ACM Conference on Electronic Commerce, pp. 140–149 (2008)Google Scholar
- 10.Elias, J., Martignon, F., Avrachenkov, K., Neglia, G.: Socially-aware network design games. In: Proc. INFOCOM 2010, pp. 41–45 (2010)Google Scholar
- 12.Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proc. 41st Annual ACM Symposium on Theory of Computing, pp. 513–522 (2009)Google Scholar
- 13.Beckmann, M., McGuire, B., Winsten, C.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)Google Scholar
- 16.Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory (2), 65–67 (1973)Google Scholar
- 17.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)Google Scholar
- 18.Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. 37th Annual ACM Symposium on Theory of Computing (2005)Google Scholar
- 19.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)Google Scholar
- 20.Osborne, M.J.: An Introduction to Game Theory. Oxford University Press, Oxford (2005)Google Scholar