IDEAS home Printed from https://ideas.repec.org/p/chu/wpaper/17-18.html
   My bibliography  Save this paper

The Optimal Defense of Networks of Targets

Author

Listed:
  • Dan Kovenock

    (Economic Science Institute, Argyros School of Business and Economics, Chapman University)

  • Brian Roberson

    (Purdue University, Department of Economics, Krannert School of Management)

Abstract

An earlier version of this paper appeared as Purdue working paper no. 1251, August 2010. We have benefited from the helpful comments of Kai Konrad and Daniel G. Arce as well as participants in conferences and seminars at Chapman University, North Carolina State University, Purdue University, Southern Methodist University, Stockholm School of Economics, Technical University of Dortmund, UC Irvine, University of Cambridge, University of East Anglia, University of Missouri, University of Pittsburgh, and University of Zurich. Part of this work was completed while Kovenock was Visiting Professor at the Social Science Research Center Berlin (WZB). Roberson gratefully acknowledges financial support from the Social Science Research Center Berlin (WZB), the Miami University Committee on Faculty Research, and the Farmer School of Business. The authors, of course, remain solely responsible for any errors or omissions

Suggested Citation

  • Dan Kovenock & Brian Roberson, 2017. "The Optimal Defense of Networks of Targets," Working Papers 17-18, Chapman University, Economic Science Institute.
  • Handle: RePEc:chu:wpaper:17-18
    as

    Download full text from publisher

    File URL: https://www.chapman.edu/research/institutes-and-centers/economic-science-institute/_files/Optimal-Defense-of-Networks-2017.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    4. 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.
    5. Sanjeev Goyal & Adrien Vigier, 2014. "Attack, Defence, and Contagion in Networks," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1518-1542.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    12. 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.
    13. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    14. 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.
    15. 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.
    16. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    17. 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.
    18. 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.
    19. Yosef Rinott & Marco Scarsini & Yaming Yu, 2012. "A Colonel Blotto Gladiator Game," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 574-590, November.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Acemoglu, Daron & Malekian, Azarakhsh & Ozdaglar, Asu, 2016. "Network security and contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 536-585.
    26. Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
    27. Dziubiński, Marcin Konrad & Goyal, Sanjeev, 2017. "How do you defend a network?," Theoretical Economics, Econometric Society, vol. 12(1), January.
    28. 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.
    29. 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.
    30. Dan Kovenock & Brian Roberson, 2010. "Conflicts with Multiple Battlefields," Purdue University Economics Working Papers 1246, Purdue University, Department of Economics.
    31. 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.
    32. 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.
    33. 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.
    34. Dziubiński, Marcin & Goyal, Sanjeev, 2013. "Network design and defence," Games and Economic Behavior, Elsevier, vol. 79(C), pages 30-43.
    35. 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.
    36. 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.
    37. 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.
    38. Powell, Robert, 2007. "Defending against Terrorist Attacks with Limited Resources," American Political Science Review, Cambridge University Press, vol. 101(3), pages 527-541, August.
    39. 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.
    40. 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.
    41. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
    42. 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.
    43. repec:wly:soecon:v:83:1:y:2016:p:105-125 is not listed on IDEAS
    44. 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.
    45. 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.
    46. Todd R. Kaplan & David Wettstein, 2006. "Caps on Political Lobbying: Comment," American Economic Review, American Economic Association, vol. 96(4), pages 1351-1354, September.
    47. 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.
    48. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    49. Ian Gale & Mark Stegeman, 1994. "Exclusion in all-pay auctions," Working Papers (Old Series) 9401, Federal Reserve Bank of Cleveland.
    50. Katz, Eliakim & Nitzan, Shmuel & Rosenberg, Jacob, 1990. "Rent-Seeking for Pure Public Goods," Public Choice, Springer, vol. 65(1), pages 49-60, April.
    51. 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.
    52. repec:oup:restud:v:81:y:2014:i:4:p:1518-1542. is not listed on IDEAS
    53. 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.
    54. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-660, May.
    55. Lee, Dongryul, 2012. "Weakest-link contests with group-specific public good prizes," European Journal of Political Economy, Elsevier, vol. 28(2), pages 238-248.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dan Kovenock & Brian Roberson, 2015. "The Optimal Defense of Network Connectivity," Working Papers 15-24, Chapman University, Economic Science Institute.
    2. 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.
    3. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    4. Dan Kovenock & Brian Roberson, 2021. "Generalizations of the General Lotto and Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 997-1032, April.
    5. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Subhasish M Chowdhury & Dan Kovenock & David Rojo Arjona & Nathaniel T Wilcox, 2021. "Focality and Asymmetry in Multi-Battle Contests," The Economic Journal, Royal Economic Society, vol. 131(636), pages 1593-1619.
    7. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 833-861, April.
    8. Shakun D. Mago & Roman M. Sheremeta, 2017. "Multi‐battle Contests: An Experimental Study," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 407-425, October.
    9. Duffy, John & Matros, Alexander, 2017. "Stochastic asymmetric Blotto games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 88-105.
    10. Kimbrough, Erik O. & Laughren, Kevin & Sheremeta, Roman, 2020. "War and conflict in economics: Theories, applications, and recent trends," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 998-1013.
    11. Deck, Cary & Sarangi, Sudipta & Wiser, Matt, 2017. "An experimental investigation of simultaneous multi-battle contests with strategic complementarities," Journal of Economic Psychology, Elsevier, vol. 63(C), pages 117-134.
    12. Subhasish M. Chowdhury & Iryna Topolyan, 2013. "The Attack-and-Defence Group Contests," University of East Anglia Applied and Financial Economics Working Paper Series 049, School of Economics, University of East Anglia, Norwich, UK..
    13. Aner Sela, 2016. "Two Stage Contests With Effort-Dependent Rewards," Working Papers 1612, Ben-Gurion University of the Negev, Department of Economics.
    14. Daniel G. Arce & Dan Kovenock J. & Brian Roberson, 2009. "Suicide Terrorism and the Weakest Link," CESifo Working Paper Series 2753, CESifo.
    15. 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.
    16. David Rietzke & Brian Roberson, 2013. "The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 937-956, April.
    17. Subhasish M. Chowdhury & Iryna Topolyan, 2015. "The Group All-Pay Auction with Heterogeneous Impact Functions," University of East Anglia Applied and Financial Economics Working Paper Series 069, School of Economics, University of East Anglia, Norwich, UK..
    18. Dan Kovenock & Sudipta Sarangi & Matt Wiser, 2015. "All-pay 2 $$\times $$ × 2 Hex: a multibattle contest with complementarities," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 571-597, August.
    19. Dongryul Lee & Joon Song, 2019. "Optimal Team Contests to Induce More Efforts," Journal of Sports Economics, , vol. 20(3), pages 448-476, April.
    20. 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.

    More about this item

    Keywords

    Allocation Game; Asymmetric Conflict; Attack and Defense; Colonel Blotto Game; Weakest-Link;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:chu:wpaper:17-18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Megan Luetje (email available below). General contact details of provider: https://edirc.repec.org/data/esichus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.