Network creation games model the creation and usage costs of networks formed by a set of selfish peers. Each peer has the ability to change the network in a limited way, e.g., by creating or deleting incident links. In doing so, a peer can reduce its individual communication cost. Typically, these costs are modeled by the maximum or average distance in the network. We introduce a generalized version of the basic network creation game (BNCG). In the BNCG (by Alon et al., SPAA 2010), each peer may replace one of its incident links by a link to an arbitrary peer. This is done in a selfish way in order to minimize either the maximum or average distance to all other peers. That is, each peer works towards a network structure that allows himself to communicate efficiently with all other peers. However, participants of large networks are seldom interested in all peers. Rather, they want to communicate efficiently only with a small subset of peers. Our model incorporates these (communication) interests explicitly. In the MAX-version, each node tries to minimize its maximum distance to nodes it is interested in. Likewise, the goal of each node in the AVG-version is to minimize the corresponding average distance.Given peers with interests and a communication network forming a tree, we prove several results on the structure and quality of equilibria in our model. For the MAX-version, we give an upper worst case bound of O ( √ n) for the private costs in an equilibrium of n peers. Moreover, we give an equilibrium for a circular interest graph where a node has private cost Ω ( √ n), showing that our bound is tight. This example can be extended such that we get a tight bound of Θ ( √ n) for the price of anarchy. For the case of general communication networks we show the price of anarchy to be Θ (n). Additionally, we prove an interesting connection between a maximum independent set in the interest graph and the private costs of the peers. For the AVG-version, we give a linear lower bound on the worst case private costs in an equilibrium.In a network creation game (NCG), several selfish players create a network by egoistic modifications of its edges. One of the most famous NCG models is due to Fabrikant et al. [6]. Their model intends to capture the dynamics in large communication and computer networks built by the individual participants (peers, players) in a selfish way: participants try to ensure a network structure supporting their own communication needs whilst limiting their individual investment into the network. Since the players do not (necessarily) cooperate, the resulting network structure may be suboptimal from a global point of view. The analysis of the resulting structure and its comparison to a (socially) optimal structure is a central aspect in the analysis of network creation games.In the original model by Fabrikant et al., players may buy (or create) a single edge for a certain (fixed) cost of α > 0. Their goal when buying edges is to improve the network structure with respect to their individual communication ...
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