Computer Science – Computer Science and Game Theory
Scientific paper
2011-05-12
Computer Science
Computer Science and Game Theory
20 pages
Scientific paper
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 Nash equilibrium. This notion is unrelated to that of the price of stability and in contrast to it is invariant under positive linear transformations of the payoff functions. 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. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game, but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is $1/(2n-3)$, that of the $n$-players public goods game is $(1-\frac{c {n})(c-1)$, where $c$ is the public good multiplier, and that of the Traveler's Dilemma game is 1/2. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite.
Apt Krzysztof R.
Schaefer Guido
No associations
LandOfFree
Selfishness Level of Strategic Games does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Selfishness Level of Strategic Games, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Selfishness Level of Strategic Games will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-496861