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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.

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The power control problem for wireless networks in the SINR model requires determining the optimal power assignment for a set of communication requests such that the SINR threshold is met for all receivers. If the network topology is known to all participants, then it is possible to compute an optimal power assignment in polynomial time. In realistic environments, however, such global knowledge is usually not available to every node. In addition, protocols that are based on global computation cannot support mobility and hardly adapt when participants dynamically join or leave the system. In this paper we present and analyze a fully distributed power control protocol that is based on local information. For a set of communication pairs, each consisting of a sender node and a designated receiver node, the algorithm enables the nodes to converge to the optimal power assignment (if there is one under the given constraints) quickly with high probability. Two types of bounded resources are considered, namely, the maximal transmission energy and the maximum distance between any sender and receiver. It is shown that the restriction to local computation increases the convergence rate by only a multiplicative factor of O(log n + log log Ψmax), where Ψmax is the maximal power constraint of the network. If the diameter of the network is bounded by Lmax then the increase in convergence rate is given by O(log n + log log Lmax).