The price of fairness and stability in resource buying games

Abstract We study the price of combining fairness and stability (PoFS) in resource buying games, in which players share the activation cost of the resources they are using. The PoFS is the ratio between the cost of a min–max fair NE profile, and the cost of a cheapest NE profile. We distinguish between games played on resources with fixed costs and load-dependent costs, and between fair cost-sharing and arbitrary cost-sharing mechanisms. We provide tight bound for the PoFS in various game classes. While in general, striving for fairness may lead to a significant increase in the social cost, we identify classes for which $$\text{ PoFS } =1$$ or is bounded by a small constant. We show that computing a min–max fair stable profile may be NP-hard even for simple classes, for which calculating a social optimum profile and a cheapest NE can be done efficiently. On the other hand, for other classes we provide optimal algorithms for calculating the min–max fair profile among the stable ones.