Selfishness Level of Strategic Games

K. Apt, G. Schäfer

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review


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. © 2012 Springer-Verlag.
Original languageEnglish
Title of host publicationAlgorithmic Game Theory
Subtitle of host publication5th International Symposium, SAGT 2012, Barcelona, Spain, October 22-23, 2012, Proceedings
EditorsMaria Serna
PublisherSpringer Verlag
Number of pages12
ISBN (Electronic)9783642339967
ISBN (Print)9783642339950
Publication statusPublished - 2012
EventInternational Symposium on Algorithmic Game Theory - Heidelberg
Duration: 22 Oct 201223 Oct 2012

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
ISSN (Print)0302-9743


ConferenceInternational Symposium on Algorithmic Game Theory

Bibliographical note

Proceedings title: Algorithmic Game Theory
Publisher: Springer
Place of publication: Heidelberg


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