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

摘要

This article investigates selfish behavior in games where players areembedded in a social context. A framework is presented which allows us tomeasure the Windfall of Friendship, i.e., how much players benefit (compared topurely selfish environments) if they care about the welfare of their friends inthe social network graph. As a case study, a virus inoculation game isexamined. We analyze the corresponding Nash equilibria and show that theWindfall of Friendship can never be negative. However, we find that if thevaluation of a friend is independent of the total number of friends, the socialwelfare may not increase monotonically with the extent to which players carefor each other; intriguingly, in the corresponding scenario where the relativeimportance of a friend declines, the Windfall is monotonic again. This articlealso studies convergence of best-response sequences. It turns out that insocial networks, convergence times are typically higher and hence constitute aprice of friendship. While such phenomena may be known on an anecdotal level,our framework allows us to quantify these effects analytically. Our formalinsights on the worst case equilibria are complemented by simulations sheddinglight onto the structure of other equilibria.