Efficient Best Response Computation for Strategic Network Formation Under Attack

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10504)


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.


  1. 1.
    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)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bala, V., Goyal, S.: A noncooperative model of network formation. Econometrica 68(5), 1181–1229 (2000)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bala, V., Goyal, S.: A strategic analysis of network reliability. Rev. Econ. Des. 5(3), 205–228 (2000). doi: 10.1007/s100580000019. ISSN 1434-4750CrossRefGoogle Scholar
  4. 4.
    Bilò, D., Gualà, L., Leucci, S., Proietti, G.: Locality-based network creation games. In: SPAA 2014, pp. 277–286 (2014)Google Scholar
  5. 5.
    Bilò, D., Gualà, L., Proietti, G.: Bounded-distance network creation games. ACM TEAC 3(3), 16:1–16:20 (2015)MathSciNetGoogle Scholar
  6. 6.
    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_12CrossRefGoogle Scholar
  7. 7.
    Chen, P.-A., David, M., Kempe, D.: Better vaccination strategies for better people. In: EC 2010, pp. 179–188. ACM (2010)Google Scholar
  8. 8.
    Cord-Landwehr, A., Lenzner, P.: Network creation games: think global - act local. In: MFCS 2015, pp. 248–260 (2015)CrossRefGoogle Scholar
  9. 9.
    Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefGoogle Scholar
  11. 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. 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. 13.
    Goyal, S., Jabbari, S., Kearns, M., Khanna, S., Morgenstern, J.: Strategic Network Formation with Attack and Immunization. arXiv preprint arXiv:1511.05196 (2015)
  14. 14.
    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_30CrossRefzbMATHGoogle Scholar
  15. 15.
    Jackson, M.O., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: SPAA 2013, pp. 83–92. ACM (2013)Google Scholar
  17. 17.
    Kliemann, L.: The price of anarchy for network formation in an adversary model. Games 2(3), 302–332 (2011)MathSciNetCrossRefGoogle Scholar
  18. 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. 19.
    Lenzner, P.: Greedy selfish network creation. In: WINE 2012, pp. 142–155 (2012)Google Scholar
  20. 20.
    Meirom, E.A., Mannor, S., Orda, A.: Formation games of reliable networks. In: INFOCOM 2015, pp. 1760–1768 (2015)Google Scholar
  21. 21.
    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_24CrossRefGoogle Scholar
  22. 22.
    Papadimitriou, C.H.: Algorithms, games, and the internet. In: STOC 2001, pp. 749–753 (2001)Google Scholar
  23. 23.
    Saha, S., Adiga, A., Vullikanti, A.K.S.: Equilibria in epidemic containment games. In: AAAI, pp. 777–783 (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Algorithm Engineering GroupHasso Plattner InstitutePotsdamGermany

Personalised recommendations