# Basic Network Creation Games with Communication Interests

## Abstract

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 with a small subset only. Our model incorporates these (communication) *interests* explicitly.

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. We focus on the MAX-version, i.e., each node tries to minimize the maximum distance to nodes it is interested in, and give an upper bound of \({\mathcal O}({\sqrt{n})}\) 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 \(\Omega({\sqrt{n})}\), showing that our bound is tight. This example can be extended such that we get a tight bound of \(\Theta({\sqrt{n})}\) for the price of anarchy. For the case of general 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.

## Keywords

Short Path Social Cost Communication Cost Social Optimum Tree Network## Preview

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## References

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