Selfishness Level of Strategic Games

  • Krzysztof R. Apt
  • Guido Schäfer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7615)


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.


Nash Equilibrium Social Welfare Social Optimum Public Good Game Congestion Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Krzysztof R. Apt
    • 1
    • 2
  • Guido Schäfer
    • 1
    • 3
  1. 1.Centrum Wiskunde & Informatica (CWI)AmsterdamThe Netherlands
  2. 2.University of AmsterdamThe Netherlands
  3. 3.VU University AmsterdamThe Netherlands

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