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.

No abstract

No abstract

This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environments. We analyze the corresponding equilibria and show that the computation of the worst and best Nash equilibrium is N P-hard. Intriguingly, even though the windfall of friendship can never be negative, the social welfare does not increase monotonically with the extent to which players care for each other. While these phenomena are known on an anecdotal level, our framework allows us to quantify these effects analytically.