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The Non-Constant-Sum Colonel Blotto Game

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  • Brian Roberson

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

  • Dmitriy Kvasov

    ()
    (School of Economics, University of Adelaide)

Abstract

The Colonel Blotto game is a two-player constant-sum game in which each player simultaneously distributes his fixed level of resources across a set of contests. In the traditional formulation of the Colonel Blotto game, the players' resources are ''use it or lose it'' in the sense that any resources which are not allocated to one of the contests are forfeited. This article examines a non-constant-sum version of the Colonel Blotto game which relaxes this use it or lose it feature. We find that if the level of asymmetry between the players' budgets is below a threshold, then there exists a one-to-one mapping from the unique set of equilibrium univariate marginal distribution functions in the constant-sum game to those in the non-constant-sum game. Once the asymmetry of the players' budgets exceeds the threshold this relationship breaks down and we construct a new equilibrium.

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Bibliographic Info

Paper provided by University of Adelaide, School of Economics in its series School of Economics Working Papers with number 2010-31.

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Length: 45 pages
Date of creation: Dec 2010
Date of revision:
Handle: RePEc:adl:wpaper:2010-31

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Keywords: Colonel Blotto Game; all-pay auction; contests; mixed strategies;

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References

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  1. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-51, June.
  2. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  3. 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.
  4. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series dp434, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, 03.
  6. Subhasish M. Chowdhury & Dan Kovenock J. & Roman M. Sheremeta, 2009. "An Experimental Investigation of Colonel Blotto Games," CESifo Working Paper Series 2688, CESifo Group Munich.
  7. Rafael Hortala-Vallve & Aniol Llorente-Saguer, 2012. "Pure strategy Nash equilibria in non-zero sum colonel Blotto games," International Journal of Game Theory, Springer, vol. 41(2), pages 331-343, May.
  8. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
  9. 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.
  10. 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, 06.
  11. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "The All-Pay Auction With Complete Information," Purdue University Economics Working Papers 1007, Purdue University, Department of Economics.
  12. Dan Kovenock & Brian Roberson, 2012. "Coalitional Colonel Blotto Games with Application to the Economics of Alliances," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(4), pages 653-676, 08.
  13. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
  14. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
  15. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-60, May.
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Citations

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Cited by:
  1. Shakun D. Mago & Roman M. Sheremeta, 2012. "Multi-Battle Contests: An Experimental Study," Working Papers 12-06, Chapman University, Economic Science Institute.
  2. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer, vol. 52(3), pages 833-861, April.
  3. John Duffy & Alexander Matros, 2013. "Stochastic Asymmetric Blotto Games: Theory and Experimental Evidence," Working Papers 509, University of Pittsburgh, Department of Economics, revised Nov 2013.
  4. Barelli, Paulo & Govindan, Srihari & Wilson, Robert, 2012. "Competition for a Majority," Research Papers 2104, Stanford University, Graduate School of Business.
  5. Daniel G. Arce & Dan Kovenock J. & Brian Roberson, 2009. "Suicide Terrorism and the Weakest Link," CESifo Working Paper Series 2753, CESifo Group Munich.
  6. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer, vol. 54(1), pages 99-129, September.
  7. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.

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