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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 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 oneto- 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 Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1252.

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Length: 46 pages
Date of creation: Aug 2010
Date of revision:
Handle: RePEc:pur:prukra:1252

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Related research

Keywords: Colonel Blotto Game; All-Pay Auction; Contests; Mixed Strategies;

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References

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  1. Baye, M.R. & Kovenock, D. & De Vries, C., 1992. "The All-Pay Auction with Complete Information," Papers 8-92-1, Pennsylvania State - Department of Economics.
  2. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer, vol. 36(3), pages 441-460, March.
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  4. Chowdhury, Subhasish M. & Kovenock, Dan & Sheremeta, Roman M., 2009. "An experimental investigation of Colonel Blotto games," Discussion Papers, Research Unit: Market Processes and Governance SP II 2009-08, Social Science Research Center Berlin (WZB).
  5. 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.
  6. Yeon-Koo Che & Ian Gale, 1998. "Caps on Political Lobbying," Microeconomics 9809003, EconWPA.
  7. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  8. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  9. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-60, May.
  10. 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.
  11. 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.
  12. 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.
  13. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
  14. 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.
  15. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
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Citations

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Cited by:
  1. 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.
  2. Shakun D. Mago & Roman M. Sheremeta, 2012. "Multi-Battle Contests: An Experimental Study," Working Papers 12-06, Chapman University, Economic Science Institute.
  3. Paulo Barelli & Srihari Govindan & Robert Wilson, 2014. "Competition for a Majority," Econometrica, Econometric Society, vol. 82(1), pages 271-314, 01.
  4. Chowdhury, Subhasish M. & Kovenock, Dan & Sheremeta, Roman M., 2009. "An experimental investigation of Colonel Blotto games," Discussion Papers, Research Unit: Market Processes and Governance SP II 2009-08, Social Science Research Center Berlin (WZB).
  5. 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.
  6. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer, vol. 54(1), pages 99-129, September.
  7. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Paper Series dp662, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  8. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.
  9. Daniel G. Arce & Dan Kovenock J. & Brian Roberson, 2009. "Suicide Terrorism and the Weakest Link," CESifo Working Paper Series 2753, CESifo Group Munich.

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