Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-10T08:41:53.116Z Has data issue: false hasContentIssue false

Strategic investment in protection in networked systems

Published online by Cambridge University Press:  03 April 2017

MATT V. LEDUC
Affiliation:
Stanford University, MS&E, 475 Via Ortega, Stanford, CA 94305-4121, USA and IIASA, Schlossplatz 1, A-2361 Laxenburg, Austria (e-mail: mattvleduc@gmail.com)
RUSLAN MOMOT
Affiliation:
INSEAD, Boulevard de Constance, 77305 Fontainebleau, France (e-mail: ruslan.momot@insead.edu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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).

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
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.
Copyright
Copyright © Cambridge University Press 2017

References

Acemoglu, D., Malekian, A., & Ozdaglar, A. (2016). Network security and contagion. Journal of Economic Theory, 166, 536585.Google Scholar
Acemoglu, D., Ozdaglar, A., & Tahbaz-Salehi, A. (2015). Systemic risk and stability in financial networks. The American Economic Review, 105 (2), 564608.Google Scholar
Arribas, I., & Salvador, A. U. (2014). Local coordination and global congestion in random networks. Discussion Papers in Economic Behaviour, University of Valencia, ERI-CES.Google Scholar
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.Google Scholar
Balthrop, J., Forrest, S., Newman, M. E. J., & Williamson, M. H. (2004). Technological networks and the spread of computer viruses. Scientific Reports, 304, 527529.Google ScholarPubMed
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.Google Scholar
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.CrossRefGoogle Scholar
Cabrales, A., Gottardi, P., & Vega-Redondo, F. (2014). Risk-sharing and contagion in networks. Ssrn 2425558.Google Scholar
Cerdeiro, D., Dziubiński, M., & Goyal, S. (2015). Contagion risk and network design. Ssrn 2619022.Google Scholar
Dziubiński, M., & Goyal, S. (2017). How do you defend a network? Theoretical Economics, 12 (1), 331376.CrossRefGoogle Scholar
Elliott, M., Golub, B., & Jackson, M. O. (2014). Financial networks and contagion. The American Economic Review, 104 (10), 31153153.Google Scholar
Finkle, J. (2015). Cyber insurance premiums rocket after high-profile attacks. Boston, MA: Reuters.Google Scholar
Gagnon, J., & Goyal, S. (2017). Networks, markets and inequality. The American Economic Review, 107 (1), 130.Google Scholar
Galeotti, A., Goyal, S., Jackson, M. O., Vega-Redondo, F., & Yariv, L. (2010). Network games. Review of Economic Studies, 77, 218244.Google Scholar
Galeotti, A., & Rogers, B. W. (2013). Strategic immunization and group structure. American Economic Journal: Microeconomics, 5 (2), 132.Google Scholar
Goyal, S., & Vigier, A. (2015). Interaction, protection and epidemics. Journal of Public Economics, 125, 6469.Google Scholar
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.Google Scholar
Heal, G., & Kunreuther, H. (2004). Interdependent security: A general model. National Bureau of Economic Research (NBER) Working Paper No. 10706. doi:10.3386/w10706.Google Scholar
Jackson, M. O. (2008). Social and economic networks. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Jackson, M. O., & Yariv, L. (2007). Diffusion of behavior and equilibrium properties in network games. American Economic Review, 97 (2), 9298.Google Scholar
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.Google Scholar
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.Google Scholar
Leduc, M. V. (2014). Mean-field models in network game theory. Ph.D. thesis, Stanford University, Stanford, USA.Google Scholar
Leduc, M. V., Jackson, M. O., & Johari, R. (2015). Pricing and referrals in diffusion on networks. preprint, arxiv:1509.06544.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Steenhuysen, J. (2015). U.S. vaccination rates high, but pockets of unvaccinated pose risk. Chicago, IL: Reuters.Google Scholar
The Economist (2015a, February 04). Rand Paul on vaccination: Resorting to freedom. The Economist, 18:42. By W.W.Google Scholar
The Economist (2015b, February 05). Politics and vaccinations: What experts say, and what people hear. The Economist, 15:47. By N.L.Google Scholar
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.Google Scholar