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Network Security and Contagion

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  • Daron Acemoglu
  • Azarakhsh Malekian
  • Asuman Ozdaglar

Abstract

We develop a theoretical model of security investments in a network of interconnected agents. Network connections introduce the possibility of cascading failures due to an exogenous or endogenous attack depending on the profile of security investments by the agents. The general presumption in the literature, based on intuitive arguments or analysis of symmetric networks, is that because security investments create positive externalities on other agents, there will be underinvestment in security. We show that this reasoning is incomplete because of a first-order economic force: security investments are also strategic substitutes. In a general (non-symmetric) network, this implies that underinvestment by some agents will encourage overinvestment by others. We demonstrate by means of examples that there can be overinvestment by some agents and also that aggregate probabilities of infection can be lower in equilibrium compared to the social optimum. We then provide sufficient conditions for underinvestment. This requires both sufficiently convex cost functions (convexity alone is not enough) and networks that are either symmetric or locally tree-like. We also characterize the impact of network structure on equilibrium and optimal investments. Finally, we show that when the attack location is endogenized (by assuming that the attacker chooses a probability distribution over the location of the attack in order to maximize damage), there is an additional incentive for overinvestment: greater investment by an agent shifts the attack to other parts of the network.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 19174.

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Date of creation: Jun 2013
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Handle: RePEc:nbr:nberwo:19174

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References

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  1. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2013. "Systemic Risk and Stability in Financial Networks," NBER Working Papers 18727, National Bureau of Economic Research, Inc.
  2. Brito, Dagobert L. & Sheshinski, Eytan & Intriligator, Michael D., 1991. "Externalities and compulsary vaccinations," Journal of Public Economics, Elsevier, vol. 45(1), pages 69-90, June.
  3. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096, April.
  5. Heski Bar-Isaac & Mariagiovanna Baccara, 2006. "How to Organize Crime," Working Papers 06-07, New York University, Leonard N. Stern School of Business, Department of Economics.
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  7. Larson, Nathan, 2011. "Network security," MPRA Paper 32822, University Library of Munich, Germany.
  8. Dan Kovenock & Brian Roberson, 2010. "The Optimal Defense of Networks of Targets," Purdue University Economics Working Papers 1251, Purdue University, Department of Economics.
  9. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  10. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406, April.
  11. Benjamin Golub & Matthew O. Jackson, 2012. "How Homophily Affects the Speed of Learning and Best-Response Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 127(3), pages 1287-1338.
  12. Geoffard, Pierre-Yves & Philipson, Tomas, 1997. "Disease Eradication: Private versus Public Vaccination," American Economic Review, American Economic Association, vol. 87(1), pages 222-30, March.
  13. de Meza, David & Gould, J R, 1992. "The Social Efficiency of Private Decisions to Enforce Property Rights," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 561-80, June.
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Cited by:
  1. Olivier Jeanne, 2014. "Macroprudential Policies in a Global Perspective," NBER Working Papers 19967, National Bureau of Economic Research, Inc.

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