On the Windfall and Price of Friendship: Inoculation Strategies on Social Networks

This article investigates selfish behavior in games where players are embedded in a social context. A framework is presented which allows us to measure the Windfall of Friendship, i.e., how much players benefit (compared to purely selfish environments) if they care about the welfare of their friends in the social network graph. As a case study, a virus inoculation game is examined. We analyze the corresponding Nash equilibria and show that the Windfall of Friendship can never be negative. However, we find that if the valuation of a friend is independent of the total number of friends, the social welfare may not increase monotonically with the extent to which players care for each other; intriguingly, in the corresponding scenario where the relative importance of a friend declines, the Windfall is monotonic again. This article also studies convergence of best-response sequences. It turns out that in social networks, convergence times are typically higher and hence constitute a pric...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Dominic Meier, Yvonne Anne Pignolet, Stefan Schmid, Roger Wattenhofer
• Keywords: CORR 2011, Education, Nash Equilibria, Network Graph, Social Welfare