Efficient Best Response Computation for Strategic Network Formation Under Attack
- 642 Downloads
Inspired by real world examples, e.g. the Internet, researchers have introduced an abundance of strategic games to study natural phenomena in networks. Unfortunately, almost all of these games have the conceptual drawback of being computationally intractable, i.e. computing a best response strategy or checking if an equilibrium is reached is NP-hard. Thus, a main challenge in the field is to find tractable realistic network formation models. We address this challenge by investigating a very recently introduced model by Goyal et al.  which focuses on robust networks in the presence of a strong adversary who attacks (and kills) nodes in the network and lets this attack spread virus-like through the network via neighboring nodes.
Our main result is to establish that this natural model is one of the few exceptions which are both realistic and computationally tractable. In particular, we answer an open question of Goyal et al. by providing an efficient algorithm for computing a best response strategy, which implies that deciding whether the game has reached a Nash equilibrium can be done efficiently as well. Our algorithm essentially solves the problem of computing a minimal connection to a network which maximizes the reachability while hedging against severe attacks on the network infrastructure and may thus be of independent interest.
- 4.Bilò, D., Gualà, L., Leucci, S., Proietti, G.: Locality-based network creation games. In: SPAA 2014, pp. 277–286 (2014)Google Scholar
- 7.Chen, P.-A., David, M., Kempe, D.: Better vaccination strategies for better people. In: EC 2010, pp. 179–188. ACM (2010)Google Scholar
- 11.Fabrikant, A., Luthra, A., Maneva, E.N., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: PODC 2003, pp. 347–351 (2003)Google Scholar
- 12.Friedrich, T., Ihde, S., Keßler, C., Lenzner, P., Neubert, S., Schumann, D.: Efficient best-response computation for strategic network formation under attack. CoRR, abs/1610.01861 (2016)Google Scholar
- 13.Goyal, S., Jabbari, S., Kearns, M., Khanna, S., Morgenstern, J.: Strategic Network Formation with Attack and Immunization. arXiv preprint arXiv:1511.05196 (2015)
- 16.Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: SPAA 2013, pp. 83–92. ACM (2013)Google Scholar
- 18.Kumar, V.A., Rajaraman, R., Sun, Z., Sundaram, R.: Existence theorems and approximation algorithms for generalized network security games. In: ICDCS 2010, pp. 348–357. IEEE (2010)Google Scholar
- 19.Lenzner, P.: Greedy selfish network creation. In: WINE 2012, pp. 142–155 (2012)Google Scholar
- 20.Meirom, E.A., Mannor, S., Orda, A.: Formation games of reliable networks. In: INFOCOM 2015, pp. 1760–1768 (2015)Google Scholar
- 22.Papadimitriou, C.H.: Algorithms, games, and the internet. In: STOC 2001, pp. 749–753 (2001)Google Scholar
- 23.Saha, S., Adiga, A., Vullikanti, A.K.S.: Equilibria in epidemic containment games. In: AAAI, pp. 777–783 (2014)Google Scholar