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Defending against multiple different attackers

Author

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  • Hausken, Kjell
  • Bier, Vicki M.

Abstract

One defender defends, and multiple heterogeneous attackers attack, an asset. Three scenarios are considered: the agents move simultaneously; the defender moves first; or the attackers move first. We show how the agents' unit costs of defense and attack, their asset evaluations, and the number of attackers influence their investments, profits, and withdrawal decisions. Withdrawal does not occur in one-period (simultaneous) games between two agents, at least with the commonly used ratio-form contest success function, but can occur in two-period games between two agents. The presence of one particularly strong attacker can cause other attackers to withdraw from the contest if the advantaged attacker appropriates so much of the defender's asset that it is no longer sufficiently attractive to interest other attackers. In such cases, the defender focuses exclusively on the strong attacker. An advantaged defender may be able to deter attacks by moving first, but will continue to suffer from attacks if moving second. This suggests the importance of proactive rather than reactive defense.

Suggested Citation

  • Hausken, Kjell & Bier, Vicki M., 2011. "Defending against multiple different attackers," European Journal of Operational Research, Elsevier, vol. 211(2), pages 370-384, June.
  • Handle: RePEc:eee:ejores:v:211:y:2011:i:2:p:370-384
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    References listed on IDEAS

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    1. J. Amegashie, 2006. "A contest success function with a tractable noise parameter," Public Choice, Springer, vol. 126(1), pages 135-144, January.
    2. Todd Sandler, 2005. "Collective versus unilateral responses to terrorism," Public Choice, Springer, vol. 124(1), pages 75-93, July.
    3. Posner, Richard A, 1975. "The Social Costs of Monopoly and Regulation," Journal of Political Economy, University of Chicago Press, vol. 83(4), pages 807-827, August.
    4. Krueger, Anne O, 1974. "The Political Economy of the Rent-Seeking Society," American Economic Review, American Economic Association, vol. 64(3), pages 291-303, June.
    5. Vicki Bier & Santiago Oliveros & Larry Samuelson, 2007. "Choosing What to Protect: Strategic Defensive Allocation against an Unknown Attacker," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 563-587, August.
    6. Keohane, Nathaniel O & Zeckhauser, Richard J, 2003. "The Ecology of Terror Defense," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 201-229, March-May.
    7. Kunreuther, Howard & Heal, Geoffrey, 2003. "Interdependent Security," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 231-249, March-May.
    8. Azaiez, M.N. & Bier, Vicki M., 2007. "Optimal resource allocation for security in reliability systems," European Journal of Operational Research, Elsevier, vol. 181(2), pages 773-786, September.
    9. Durham, Yvonne & Hirshleifer, Jack & Smith, Vernon L., 2008. "The Paradox of Power," Handbook of Experimental Economics Results, Elsevier.
    10. Kjell Hausken, 2004. "Mutual Raiding of Production and the Emergence of Exchange," Economic Inquiry, Western Economic Association International, vol. 42(4), pages 572-586, October.
    11. Halvor Mehlum & Karl Moene, 2006. "Fighting against the odds," Economics of Governance, Springer, vol. 7(1), pages 75-87, January.
    12. Kjell Hausken, 2005. "Production and Conflict Models Versus Rent-Seeking Models," Public Choice, Springer, vol. 123(1), pages 59-93, April.
    13. Durham, Yvonne & Hirshleifer, Jack & Smith, Vernon L, 1998. "Do the Rich Get Richer and the Poor Poorer? Experimental Tests of a Model of Power," American Economic Review, American Economic Association, vol. 88(4), pages 970-983, September.
    14. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    15. Zhuang, Jun & Bier, Vicki M. & Alagoz, Oguzhan, 2010. "Modeling secrecy and deception in a multiple-period attacker-defender signaling game," European Journal of Operational Research, Elsevier, vol. 203(2), pages 409-418, June.
    16. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    17. Jack Hirshleifer, 1989. "Conflict and rent-seeking success functions: Ratio vs. difference models of relative success," Public Choice, Springer, vol. 63(2), pages 101-112, November.
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    Citations

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    Cited by:

    1. Xing Gao & Weijun Zhong & Shue Mei, 2013. "Information Security Investment When Hackers Disseminate Knowledge," Decision Analysis, INFORMS, vol. 10(4), pages 352-368, December.
    2. Zhang, Chi & Ramirez-Marquez, José Emmanuel & Wang, Jianhui, 2015. "Critical infrastructure protection using secrecy – A discrete simultaneous game," European Journal of Operational Research, Elsevier, vol. 242(1), pages 212-221.
    3. Xing Gao & Weijun Zhong & Shue Mei, 2014. "A game-theoretic analysis of information sharing and security investment for complementary firms," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(11), pages 1682-1691, November.
    4. Deck, Cary & Foster, Joshua & Song, Hongwei, 2015. "Defense against an opportunistic challenger: Theory and experiments," European Journal of Operational Research, Elsevier, vol. 242(2), pages 501-513.
    5. repec:eee:reensy:v:169:y:2018:i:c:p:51-62 is not listed on IDEAS
    6. Ioannidis, Christos & Pym, David & Williams, Julian, 2012. "Information security trade-offs and optimal patching policies," European Journal of Operational Research, Elsevier, vol. 216(2), pages 434-444.
    7. repec:eee:reensy:v:165:y:2017:i:c:p:292-301 is not listed on IDEAS
    8. Ye, Zhi-Sheng & Peng, Rui & Wang, Wenbin, 2017. "Defense and attack of performance-sharing common bus systemsAuthor-Name: Zhai, Qingqing," European Journal of Operational Research, Elsevier, vol. 256(3), pages 962-975.
    9. Ríos Insua, David & Cano, Javier & Pellot, Michael & Ortega, Ricardo, 2016. "Multithreat multisite protection: A security case study," European Journal of Operational Research, Elsevier, vol. 252(3), pages 888-899.
    10. repec:eee:ejores:v:266:y:2018:i:3:p:920-933 is not listed on IDEAS
    11. Gallice, Andrea, 2017. "An approximate solution to rent-seeking contests with private information," European Journal of Operational Research, Elsevier, vol. 256(2), pages 673-684.

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