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Interplay between Security Providers, Consumers, and Attackers: A Weighted Congestion Game Approach

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Decision and Game Theory for Security (GameSec 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7037))

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Abstract

Network users can choose among different security solutions to protect their data. Those solutions are offered by competing providers, with possibly different performance and price levels. In this paper, we model the interactions among users as a noncooperative game, with a negative externality coming from the fact that attackers target popular systems to maximize their expected gain. Using a nonatomic weighted congestion game model for user interactions, we prove the existence and uniqueness of a user equilibrium, and exhibit the tractability of its computation, as a solution of a convex problem. We also compute the corresponding Price of Anarchy, that is the loss of efficiency due to user selfishness, and investigate some consequences for the (higher-level) pricing game played by security providers.

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References

  1. Alpcan, T., Başar, T.: Network Security: A Decision and Game Theoretic Approach. Cambridge University Press (2011)

    Google Scholar 

  2. Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the economics of transportation. Yale University Press, New Heaven (1956)

    Google Scholar 

  3. Berge, C.: Espaces topologiques. Fonctions multivoques, Collection Universitaire de Mathématiques, Dunod, Paris, vol. III (1959)

    Google Scholar 

  4. Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted Congestion Games: Price of Anarchy, Universal Worst-Case Examples, and Tightness. In: de Berg, M., Meyer, U. (eds.) ESA 2010. LNCS, vol. 6347, pp. 17–28. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Bistarelli, S., Dall’Aglio, M., Peretti, P.: Strategic Games on Defense Trees. In: Dimitrakos, T., Martinelli, F., Ryan, P.Y.A., Schneider, S. (eds.) FAST 2006. LNCS, vol. 4691, pp. 1–15. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Bohacek, N., Hespanha, J.P., Lee, J., Lim, C., Obraczka, K.: Game theoretic stochastic routing for fault tolerance and security in computer networks. IEEE Transactions on Parallel and Distributed Systems 18(9), 1227–1240 (2007)

    Article  Google Scholar 

  7. Correa, J.R., Schulz, A.S., Stier-Moses, N.: A geometric approach to the price of anarchy in nonatomic congestion games. Games and Economic Behavior 64(2), 457–469 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cremonini, M., Nizovtsev, D.: Understanding and influencing attackers’ decisions: Implications for security investment strategies. In: Proc. of 5th Workshop on the Economics of Information Security (WEIS), Cambridge, UK (2006)

    Google Scholar 

  9. Fudenberg, D., Maskin, E.: The folk theorem in repeated games with discounting or with incomplete information. Econometrica 54(3), 533–554 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fudenberg, D., Tirole, J.: Game Theory. MIT Press (1991)

    Google Scholar 

  11. Ganesh, A., Gunawardena, D., Jey, P., Massoulié, L., Scott, J.: Efficient quarantining of scanning worms: Optimal detection and co-ordination. In: Proc. of IEEE INFOCOM 2006, Barcelona, Spain (2006)

    Google Scholar 

  12. Jiang, L., Anantharam, V., Walrand, J.: Efficiency of selfish investments in network security. In: Proc. of 3rd Workshop on the Economics of Networks, Systems, and Computation, Seattle, WA, USA (2008)

    Google Scholar 

  13. Johari, R., Weintraub, G.Y., Van Roy, B.: Investment and market structure in industries with congestion. Operations Research 58(5), 1303–1317 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  14. Karakostas, G., Kolliopoulos, S.G.: Edge pricing of multicommodity networks for heterogeneous selfish users. In: Proc. of FOCS, pp. 268–276 (2004)

    Google Scholar 

  15. Kodialam, M., Lakshman, T.V.: Detecting network intrusions via sampling: A game theoretic approach. In: Proc. of IEEE INFOCOM, San Francisco, CA, USA (2003)

    Google Scholar 

  16. Koutsoupias, E., Papadimitriou, C.: Worst-Case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  17. Lelarge, M., Bolot, J.: Economic incentives to increase security in the internet: The case for insurance. In: Proc. of IEEE INFOCOM, Rio de Janeiro, Brazil (2009)

    Google Scholar 

  18. Maillé, P., Reichl, P., Tuffin, B.: Of threats and costs: A game-theoretic approach to security risk management. In: Gülpınar, N., Harrison, P., Rüstem, B. (eds.) Performance Models and Risk Management in Communication Systems. Springer, Heidelberg (2010)

    Google Scholar 

  19. Mavronicolas, M., Milchtaich, I., Monien, B., Tiemann, K.: Congestion Games with Player-Specific Constants. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 633–644. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Milchtaich, I.: Congestion games with player-specific payoff functions. Games and Economic Behavior 13(1), 111–124 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  21. Milchtaich, I.: Weighted congestion games with separable preferences. Games and Economic Behavior 67(2), 750–757 (2009), http://www.sciencedirect.com/science/article/B6WFW-4W0SK2D-1/2/63c8ccc38f57d26ba8db4ed12c1596d3

    Article  MATH  MathSciNet  Google Scholar 

  22. Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behaviour 14, 124–143 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press (1994)

    Google Scholar 

  24. Perakis, G.: The “Price of Anarchy” under nonlinear and asymmetric costs. Mathematics of Operations Research 32(3), 614–628 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  25. Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press (2005)

    Google Scholar 

  26. Roughgarden, T., Tardos, E.: Bounding the inefficiency of equilibria in nonatomic congestion games. Games and Economic Behavior 47(2), 389–403 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Sandholm, W.H.: Potential games with continuous player sets. Journal of Economic Theory 97(1), 81–108 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  28. Sandholm, W.H.: Large population potential games. Journal of Economic Theory 144(4), 1710–1725 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  29. Schmeidler, D.: Equilibrium points of nonatomic games. Journal of Statistical Physics 7(4), 295–300 (1973)

    Article  MATH  MathSciNet  Google Scholar 

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Maillé, P., Reichl, P., Tuffin, B. (2011). Interplay between Security Providers, Consumers, and Attackers: A Weighted Congestion Game Approach. In: Baras, J.S., Katz, J., Altman, E. (eds) Decision and Game Theory for Security. GameSec 2011. Lecture Notes in Computer Science, vol 7037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25280-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-25280-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25279-2

  • Online ISBN: 978-3-642-25280-8

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