The Impact of Social Ignorance on Weighted Congestion Games

We consider weighted linear congestion games, and investigate how social ignorance, namely lack of information about the presence of some players, affects the inefficiency of pure Nash equilibria (PNE) and the convergence rate of the ε-Nash dynamics. To this end, we adopt the model of graphical linear congestion games with weighted players, where the individual cost and the strategy selection of each player only depends on his neighboring players in the social graph. We show that such games admit a potential function, and thus a PNE. Our main result is that the impact of social ignorance on the Price of Anarchy (PoA) and the Price of Stability (PoS) is naturally quantified by the independence number α(G) of the social graph G. In particular, we show that the PoA grows roughly as α(G)(α(G) + 2), which is essentially tight as long as α(G) does not exceed half the number of players, and that the PoS lies between α(G) and 2α(G). Moreover, we show that the ε-Nash dynamics reaches ...

• Type: Conference
• Year: 2009
• Where: WINE
• Authors: Dimitris Fotakis, Vasilis Gkatzelis, Alexis C. Kaporis, Paul G. Spirakis
• Keywords: Economy, Linear Congestion Games, Social Graph, WINE 2009, ε-Nash Dynamics