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The Non-Constant-Sum Colonel Blotto Game

  • Brian Roberson


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

  • Dmitriy Kvasov


    (School of Economics, University of Adelaide)

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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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
Contact details of provider: Postal: Adelaide SA 5005
Phone: (618) 8303 5540
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  1. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  2. Kovenock, Dan & Roberson, Brian, 2008. "Coalitional Colonel Blotto games with application to the economics of alliances
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  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.
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  6. Michael R. Baye & Dan Kovenock & Casper G. de Vries, 2009. "Contests with Rank-Order Spillovers," Tinbergen Institute Discussion Papers 09-066/2, Tinbergen Institute.
  7. 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.
  8. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
  9. 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.
  10. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
  11. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
  12. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
  13. 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.
  14. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-51, June.
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