Basic Network Creation Games with Communication Interests

A. Cord-Landwehr, M. Huellmann (married name: Eikel), P. Kling, A. Setzer, in: Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT), 2012, pp. 72--83.

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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 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 Theta(n).Additionally, we prove an interesting connection between a maximum independent set in the interest graph and the private costs of the peers.
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Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT)
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72--83
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Cord-Landwehr A, Huellmann (married name: Eikel) M, Kling P, Setzer A. Basic Network Creation Games with Communication Interests. In: Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT). LNCS. ; 2012:72--83. doi:10.1007/978-3-642-33996-7_7
Cord-Landwehr, A., Huellmann (married name: Eikel), M., Kling, P., & Setzer, A. (2012). Basic Network Creation Games with Communication Interests. In Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT) (pp. 72--83). https://doi.org/10.1007/978-3-642-33996-7_7
@inproceedings{Cord-Landwehr_Huellmann (married name: Eikel)_Kling_Setzer_2012, series={LNCS}, title={Basic Network Creation Games with Communication Interests}, DOI={10.1007/978-3-642-33996-7_7}, booktitle={Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT)}, author={Cord-Landwehr, Andreas and Huellmann (married name: Eikel), Martina and Kling, Peter and Setzer, Alexander}, year={2012}, pages={72--83}, collection={LNCS} }
Cord-Landwehr, Andreas, Martina Huellmann (married name: Eikel), Peter Kling, and Alexander Setzer. “Basic Network Creation Games with Communication Interests.” In Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT), 72--83. LNCS, 2012. https://doi.org/10.1007/978-3-642-33996-7_7.
A. Cord-Landwehr, M. Huellmann (married name: Eikel), P. Kling, and A. Setzer, “Basic Network Creation Games with Communication Interests,” in Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT), 2012, pp. 72--83.
Cord-Landwehr, Andreas, et al. “Basic Network Creation Games with Communication Interests.” Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT), 2012, pp. 72--83, doi:10.1007/978-3-642-33996-7_7.
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