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The Non-Constant-Sum Colonel Blotto Game

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  • Brian Roberson
  • Dmitriy Kvasov

Abstract

The Colonel Blotto game is a two-player constant-sum game in which each player simultaneously distributes her 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 paper 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 the unique set of equilibrium univariate marginal distributions of the non-constant-sum game is equivalent up to an affine transformation to the unique set of equilibrium univariate marginal distributions of the constant-sum game. Once the asymmetry of the players’ budgets exceeds the threshold we construct a new equilibrium.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2378.

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Date of creation: 2008
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Handle: RePEc:ces:ceswps:_2378

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Keywords: Colonel Blotto game; all-pay auction; contests;

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References

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  1. 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.
  2. Chowdhury, Subhasish & Kovenock, Dan & Sheremeta, Roman, 2011. "An Experimental Investigation of Colonel Blotto Games," MPRA Paper 46810, University Library of Munich, Germany.
  3. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  4. 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.
  5. Dan Kovenock & Brian Roberson, 2007. "Coalitional Colonel Blotto Games with Application to the Economics of Alliances," Purdue University Economics Working Papers 1207, Purdue University, Department of Economics.
  6. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
  7. Baye, M. & Kovenock, D. & Vries, C. de, 1990. "The All-Pay Auction with Complete Information," Discussion Paper 1990-51, Tilburg University, Center for Economic Research.
  8. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  9. Yeon-Koo Che & Ian Gale, 1998. "Caps on Political Lobbying," Microeconomics 9809003, EconWPA.
  10. 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.
  11. 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.
  12. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
  13. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-60, May.
  14. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
  15. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
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Cited by:
  1. Chowdhury, Subhasish & Kovenock, Dan & Sheremeta, Roman, 2011. "An Experimental Investigation of Colonel Blotto Games," MPRA Paper 46810, University Library of Munich, Germany.
  2. 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.
  3. Daniel G. Arce & Dan Kovenock J. & Brian Roberson, 2009. "Suicide Terrorism and the Weakest Link," CESifo Working Paper Series 2753, CESifo Group Munich.
  4. Shakun D. Mago & Roman M. Sheremeta, 2012. "Multi-Battle Contests: An Experimental Study," Working Papers 12-06, Chapman University, Economic Science Institute.
  5. Paulo Barelli & Srihari Govindan & Robert Wilson, 2012. "Competition For A Majority," Levine's Working Paper Archive 786969000000000445, David K. Levine.
  6. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.
  7. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer, vol. 54(1), pages 99-129, September.

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