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Strategic investment in protection in networked systems

  • MATT V. LEDUC (a1) and RUSLAN MOMOT (a2)
Abstract

We study the incentives that agents have to invest in costly protection against cascading failures in networked systems. Applications include vaccination, computer security, and airport security. Agents are connected through a network and can fail either intrinsically or as a result of the failure of a subset of their neighbors. We characterize the equilibrium based on an agent's failure probability and derive conditions under which equilibrium strategies are monotone in degree (i.e. in how connected an agent is on the network). We show that different kinds of applications (e.g. vaccination, malware, airport/EU security) lead to very different equilibrium patterns of investments in protection, with important welfare and risk implications. Our equilibrium concept is flexible enough to allow for comparative statics in terms of network properties, and we show that it is also robust to the introduction of global externalities (e.g. price feedback, congestion).

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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
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Acemoglu, D., Malekian, A., & Ozdaglar, A. (2016). Network security and contagion. Journal of Economic Theory, 166, 536585.
Acemoglu, D., Ozdaglar, A., & Tahbaz-Salehi, A. (2015). Systemic risk and stability in financial networks. The American Economic Review, 105 (2), 564608.
Arribas, I., & Salvador, A. U. (2014). Local coordination and global congestion in random networks. Discussion Papers in Economic Behaviour, University of Valencia, ERI-CES.
Aspnes, J., Chang, K., & Yampolskiy, A. (2006). Inoculation strategies for victims of viruses and the sum-of-squares partition problem. Journal of Computer and System Sciences, 72 (6), 10771093.
Balthrop, J., Forrest, S., Newman, M. E. J., & Williamson, M. H. (2004). Technological networks and the spread of computer viruses. Scientific Reports, 304, 527529.
Benjamin, J., Böhme, R., & Grossklags, J. (2011). Security games with market insurance. Decision and game theory for security. Proceedings of the Second International Conference, GameSec 2011 (pp. 117–130). Berlin: Springer.
Blume, L., Easley, D., Kleinberg, J., Kleinberg, R., & Tardos, É. (2013). Network formation in the presence of contagious risk. ACM Transactions on Economics and Computation, 1 (2), 6.
Cabrales, A., Gottardi, P., & Vega-Redondo, F. (2014). Risk-sharing and contagion in networks. Ssrn 2425558.
Cerdeiro, D., Dziubiński, M., & Goyal, S. (2015). Contagion risk and network design. Ssrn 2619022.
Dziubiński, M., & Goyal, S. (2017). How do you defend a network? Theoretical Economics, 12 (1), 331376.
Elliott, M., Golub, B., & Jackson, M. O. (2014). Financial networks and contagion. The American Economic Review, 104 (10), 31153153.
Finkle, J. (2015). Cyber insurance premiums rocket after high-profile attacks. Boston, MA: Reuters.
Gagnon, J., & Goyal, S. (2017). Networks, markets and inequality. The American Economic Review, 107 (1), 130.
Galeotti, A., Goyal, S., Jackson, M. O., Vega-Redondo, F., & Yariv, L. (2010). Network games. Review of Economic Studies, 77, 218244.
Galeotti, A., & Rogers, B. W. (2013). Strategic immunization and group structure. American Economic Journal: Microeconomics, 5 (2), 132.
Goyal, S., & Vigier, A. (2015). Interaction, protection and epidemics. Journal of Public Economics, 125, 6469.
Heal, G., Kearns, M., Kleindorfer, P., & Kunreuther, H. (2006). Interdependent security in interconnected networks. In Seeds of disaster, roots of response: How private action can reduce public vulnerability (pp. 258275). Cambridge University Press.
Heal, G., & Kunreuther, H. (2004). Interdependent security: A general model. National Bureau of Economic Research (NBER) Working Paper No. 10706. doi:10.3386/w10706.
Jackson, M. O. (2008). Social and economic networks. Princeton, NJ: Princeton University Press.
Jackson, M. O., & Yariv, L. (2007). Diffusion of behavior and equilibrium properties in network games. American Economic Review, 97 (2), 9298.
Jackson, M. O., & Zenou, Y. (2014). Games on networks. In Young, P., & Zamir, S. (Eds.), Handbook of game theory, vol. 4. Amsterdam: Elsevier, pp. 91157.
Johnson, B., Böhme, R., & Grossklags, J. (2011). Security games with market insurance. Decision and game theory for security. Proceedings of the Second International Conference, GameSec 2011 (pp. 117130). Berlin: Springer.
Leduc, M. V. (2014). Mean-field models in network game theory. Ph.D. thesis, Stanford University, Stanford, USA.
Leduc, M. V., Jackson, M. O., & Johari, R. (2015). Pricing and referrals in diffusion on networks. preprint, arxiv:1509.06544.
Lelarge, M., & Bolot, J. (2008a). A local mean field analysis of security investments in networks. Proceedings of the 3rd International Workshop on Economics of Networked Systems, SIGCOMM ACM Special Interest Group on Data Communication, ACM, New York, NY, pp. 25–30.
Lelarge, M., & Bolot, J. (2008b). Network externalities and the deployment of security features and protocols in the internet. Proceedings of the 2008 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, ACM, New York, NY, pp. 37–48.
Lelarge, M., & Bolot, J. (2009). Economic incentives to increase security in the internet: The case for insurance. IEEE INFOCOM 2009 (pp. 1494–1502). Rio de Janeiro.
Rosas-Casals, M., Valverde, S., & Solé, R. V. (2007). Topological vulnerability of the european power grid under errors and attacks. International Journal of Bifurcation and Chaos, 17 (7), 24652475.
Steenhuysen, J. (2015). U.S. vaccination rates high, but pockets of unvaccinated pose risk. Chicago, IL: Reuters.
The Economist (2015a, February 04). Rand Paul on vaccination: Resorting to freedom. The Economist, 18:42. By W.W.
The Economist (2015b, February 05). Politics and vaccinations: What experts say, and what people hear. The Economist, 15:47. By N.L.
Wang, Z., Scaglione, A., & Thomas, R. J. (2010). The node degree distribution in power grid and its topology robustness under random and selective node removals. In Communications Workshops (ICC), 2010 IEEE International Conference on IEEE, pp. 1–5.
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Network Science
  • ISSN: 2050-1242
  • EISSN: 2050-1250
  • URL: /core/journals/network-science
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