Algorithmic Game Theory pp 72-83 | Cite as

# 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

- 1.Albers, S., Eilts, S., Even-Dar, E., Mansour, Y., Roditty, L.: On nash equilibria for a network creation game. In: 17th SODA, pp. 89–98. ACM (2006)Google Scholar
- 2.Alon, N., Demaine, E.D., Hajiaghayi, M.T., Leighton, T.: Basic network creation games. In: 22nd SPAA, pp. 106–113. ACM (2010)Google Scholar
- 3.Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: 45th FOCS, pp. 295–304. IEEE (2004)Google Scholar
- 4.Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. In: 35th STOC, pp. 511–520. ACM (2003)Google Scholar
- 5.Cord-Landwehr, A., Hüllmann, M., Kling, P., Setzer, A.: Basic network creation games with communication interests. CoRR, arxiv.org/abs/1207.5419 (2012)Google Scholar
- 6.Demaine, E.D., Hajiaghayi, M.T., Mahini, H., Zadimoghaddam, M.: The price of anarchy in network creation games. In: 26th PODC, pp. 292–298. ACM (2007)Google Scholar
- 7.Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: 22nd PODC, pp. 347–351. ACM (2003)Google Scholar
- 8.Halevi, Y., Mansour, Y.: A Network Creation Game with Nonuniform Interests. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 287–292. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 9.Koutsoupias, E., Papadimitriou, C.: Worst-Case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
- 10.Lenzner, P.: On Dynamics in Basic Network Creation Games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 254–265. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 11.Mihalák, M., Schlegel, J.C.: The Price of Anarchy in Network Creation Games Is (Mostly) Constant. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 276–287. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 12.Monderer, D., Shapley, L.S.: Potential Games. Games and Economic Behavior 14(1), 124–143 (1996)MATHMathSciNetCrossRefGoogle Scholar