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The Optimal Defense of Networks of Targets

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  • Dan Kovenock
  • Brian Roberson

Abstract

This paper examines a game-theoretic model of attack and defense of multiple networks of targets in which there exist intra-network strategic complementarities among targets. The defender s objective is to successfully defend all of the networks and the attacker s objective is to successfully attack at least one network of targets. In this context, our results highlight the importance of modeling asymmetric attack and defense as a conflict between fully strategic actors with endogenous entry and force expenditure decisions as well as allowing for general correlation structures for force expenditures within and across the networks of targets.

Suggested Citation

  • Dan Kovenock & Brian Roberson, 2010. "The Optimal Defense of Networks of Targets," Purdue University Economics Working Papers 1251, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1251
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    1. Weinstein Jonathan, 2012. "Two Notes on the Blotto Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-13, March.
    2. Hortala-Vallve, Rafael & Llorente-Saguer, Aniol, 2010. "A simple mechanism for resolving conflict," Games and Economic Behavior, Elsevier, vol. 70(2), pages 375-391, November.
    3. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    4. Brian Roberson & Dmitriy Kvasov, 2012. "The non-constant-sum Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 397-433, October.
    5. Hausken, Kjell, 2008. "Strategic defense and attack for series and parallel reliability systems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 856-881, April.
    6. Konrad, Kai A., 2002. "Investment in the absence of property rights; the role of incumbency advantages," European Economic Review, Elsevier, vol. 46(8), pages 1521-1537, September.
    7. Boyer, Pierre C. & Konrad, Kai A. & Roberson, Brian, 2017. "Targeted campaign competition, loyal voters, and supermajorities," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 49-62.
    8. Sanjeev Goyal & Adrien Vigier, 2014. "Attack, Defence, and Contagion in Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1518-1542.
    9. 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.
    10. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    11. Kyung Baik, 2008. "Contests with group-specific public-good prizes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 103-117, January.
    12. Yosef Rinott & Marco Scarsini & Yaming Yu, 2012. "A Colonel Blotto Gladiator Game," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 574-590, November.
    13. 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.
    14. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    15. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    16. Dan Kovenock & Brian Roberson, 2010. "Conflicts with Multiple Battlefields," Purdue University Economics Working Papers 1246, Purdue University, Department of Economics.
    17. Baik, Kyung Hwan & Kim, In-Gyu & Na, Sunghyun, 2001. "Bidding for a group-specific public-good prize," Journal of Public Economics, Elsevier, vol. 82(3), pages 415-429, December.
    18. Dziubiński, Marcin & Goyal, Sanjeev, 2013. "Network design and defence," Games and Economic Behavior, Elsevier, vol. 79(C), pages 30-43.
    19. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
    20. Powell, Robert, 2007. "Defending against Terrorist Attacks with Limited Resources," American Political Science Review, Cambridge University Press, vol. 101(3), pages 527-541, August.
    21. Jack Hirshleifer, 1983. "From weakest-link to best-shot: The voluntary provision of public goods," Public Choice, Springer, vol. 41(3), pages 371-386, January.
    22. Szentes, Balazs & Rosenthal, Robert W., 2003. "Three-object two-bidder simultaneous auctions: chopsticks and tetrahedra," Games and Economic Behavior, Elsevier, vol. 44(1), pages 114-133, July.
    23. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
    24. Britta Hoyer & Kris De Jaegher, 2016. "Strategic Network Disruption and Defense," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(5), pages 802-830, October.
    25. repec:wly:soecon:v:83:1:y:2016:p:105-125 is not listed on IDEAS
    26. Chowdhury, Subhasish M. & Lee, Dongryul & Sheremeta, Roman M., 2013. "Top guns may not fire: Best-shot group contests with group-specific public good prizes," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 94-103.
    27. Powell, Robert, 2007. "Allocating Defensive Resources with Private Information about Vulnerability," American Political Science Review, Cambridge University Press, vol. 101(4), pages 799-809, November.
    28. Dan Kovenock & Brian Roberson, 2018. "The Optimal Defense Of Networks Of Targets," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2195-2211, October.
    29. Acemoglu, Daron & Malekian, Azarakhsh & Ozdaglar, Asu, 2016. "Network security and contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 536-585.
    30. Ian Gale & Mark Stegeman, 1994. "Exclusion in all-pay auctions," Working Papers (Old Series) 9401, Federal Reserve Bank of Cleveland.
    31. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    32. repec:oup:restud:v:81:y:2014:i:4:p:1518-1542. is not listed on IDEAS
    33. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-660, May.
    34. Iryna Topolyan, 2014. "Rent-seeking for a public good with additive contributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 465-476, February.
    35. Sanjeev Goyal & Adrien Vigier, 2014. "Attack, Defence, and Contagion in Networks," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1518-1542.
    36. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
    37. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    38. Yeon-Koo Che & Ian L. Gale, 2006. "Caps on Political Lobbying: Reply," American Economic Review, American Economic Association, vol. 96(4), pages 1355-1360, September.
    39. Kolmar, Martin & Rommeswinkel, Hendrik, 2013. "Contests with group-specific public goods and complementarities in efforts," Journal of Economic Behavior & Organization, Elsevier, vol. 89(C), pages 9-22.
    40. Rafael Hortala-Vallve & Aniol Llorente-Saguer, 2012. "Pure strategy Nash equilibria in non-zero sum colonel Blotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 331-343, May.
    41. Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
    42. Dziubiński, Marcin Konrad & Goyal, Sanjeev, 2017. "How do you defend a network?," Theoretical Economics, Econometric Society, vol. 12(1), January.
    43. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    44. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
    45. Scott Macdonell & Nick Mastronardi, 2015. "Waging simple wars: a complete characterization of two-battlefield Blotto equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 183-216, January.
    46. Bernhardt, Dan & Polborn, Mattias K., 2010. "Non-convexities and the gains from concealing defenses from committed terrorists," Economics Letters, Elsevier, vol. 107(1), pages 52-54, April.
    47. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    48. Caroline D. Thomas, 2009. "N-Dimensional Blotto Game with Asymmetric Battlefield Values," Department of Economics Working Papers 130116, The University of Texas at Austin, Department of Economics, revised Dec 2016.
    49. Brian Roberson, 2008. "Pork-Barrel Politics, Targetable Policies, and Fiscal Federalism," Journal of the European Economic Association, MIT Press, vol. 6(4), pages 819-844, June.
    50. Todd R. Kaplan & David Wettstein, 2006. "Caps on Political Lobbying: Comment," American Economic Review, American Economic Association, vol. 96(4), pages 1351-1354, September.
    51. B. Peter Rosendorff & Todd Sandler, 2004. "Too Much of a Good Thing?," Journal of Conflict Resolution, Peace Science Society (International), vol. 48(5), pages 657-671, October.
    52. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    53. Katz, Eliakim & Nitzan, Shmuel & Rosenberg, Jacob, 1990. "Rent-Seeking for Pure Public Goods," Public Choice, Springer, vol. 65(1), pages 49-60, April.
    54. Szentes, Balazs & Rosenthal, Robert W., 2003. "Beyond chopsticks: Symmetric equilibria in majority auction games," Games and Economic Behavior, Elsevier, vol. 45(2), pages 278-295, November.
    55. Daniel G. Arce & Dan Kovenock & Brian Roberson, 2012. "Weakest‐link attacker‐defender games with multiple attack technologies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 457-469, September.
    56. Lee, Dongryul, 2012. "Weakest-link contests with group-specific public good prizes," European Journal of Political Economy, Elsevier, vol. 28(2), pages 238-248.
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    More about this item

    Keywords

    Asymmetric Conflict; Attack and Defense; Weakest-Link; Best-Shot;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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    This paper has been announced in the following NEP Reports:

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