  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
price of friendship. While such phenomena may be known on an anecdotal level,
our framework allows us to quantify these effects analytically. Our formal
insights on the worst case equilibria are complemented by simulations shedding
light onto the structure of other equilibria.
