Abstract
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. [14] 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.
This is a preview of subscription content, log in via an institution.
References
Aspnes, J., Chang, K., Yampolskiy, A.: Inoculation strategies for victims of viruses and the sum-of-squares partition problem. J. Comput. Syst. Sci. 72(6), 1077–1093 (2006)
Bala, V., Goyal, S.: A noncooperative model of network formation. Econometrica 68(5), 1181–1229 (2000)
Bala, V., Goyal, S.: A strategic analysis of network reliability. Rev. Econ. Des. 5(3), 205–228 (2000). doi:10.1007/s100580000019. ISSN 1434-4750
Bilò, D., Gualà, L., Leucci, S., Proietti, G.: Locality-based network creation games. In: SPAA 2014, pp. 277–286 (2014)
Bilò, D., Gualà, L., Proietti, G.: Bounded-distance network creation games. ACM TEAC 3(3), 16:1–16:20 (2015)
Chauhan, A., Lenzner, P., Melnichenko, A., Münn, M.: On selfish creation of robust networks. In: Gairing, M., Savani, R. (eds.) SAGT 2016. LNCS, vol. 9928, pp. 141–152. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53354-3_12
Chen, P.-A., David, M., Kempe, D.: Better vaccination strategies for better people. In: EC 2010, pp. 179–188. ACM (2010)
Cord-Landwehr, A., Lenzner, P.: Network creation games: think global - act local. In: MFCS 2015, pp. 248–260 (2015)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, Heidelberg (2013)
Ehsani, S., Fadaee, S.S., Fazli, M., Mehrabian, A., Sadeghabad, S.S., Safari, M.A., Saghafian, M.: A bounded budget network creation game. ACM Trans. Algorithms 11(4), 34 (2015)
Fabrikant, A., Luthra, A., Maneva, E.N., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: PODC 2003, pp. 347–351 (2003)
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)
Goyal, S., Jabbari, S., Kearns, M., Khanna, S., Morgenstern, J.: Strategic Network Formation with Attack and Immunization. arXiv preprint arXiv:1511.05196 (2015)
Goyal, S., Jabbari, S., Kearns, M., Khanna, S., Morgenstern, J.: Strategic network formation with attack and immunization. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 429–443. Springer, Heidelberg (2016). doi:10.1007/978-3-662-54110-4_30
Jackson, M.O., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)
Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: SPAA 2013, pp. 83–92. ACM (2013)
Kliemann, L.: The price of anarchy for network formation in an adversary model. Games 2(3), 302–332 (2011)
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)
Lenzner, P.: Greedy selfish network creation. In: WINE 2012, pp. 142–155 (2012)
Meirom, E.A., Mannor, S., Orda, A.: Formation games of reliable networks. In: INFOCOM 2015, pp. 1760–1768 (2015)
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). doi:10.1007/978-3-642-16170-4_24
Papadimitriou, C.H.: Algorithms, games, and the internet. In: STOC 2001, pp. 749–753 (2001)
Saha, S., Adiga, A., Vullikanti, A.K.S.: Equilibria in epidemic containment games. In: AAAI, pp. 777–783 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Friedrich, T., Ihde, S., Keßler, C., Lenzner, P., Neubert, S., Schumann, D. (2017). Efficient Best Response Computation for Strategic Network Formation Under Attack. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-66700-3_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66699-0
Online ISBN: 978-3-319-66700-3
eBook Packages: Computer ScienceComputer Science (R0)