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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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File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2010-31.pdf
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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
Web page: http://www.economics.adelaide.edu.au/

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  1. Michael Baye & Dan Kovenock & Casper Vries, 2012. "Contests with rank-order spillovers," Economic Theory, Springer, vol. 51(2), pages 315-350, October.
  2. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-51, June.
  3. Chowdhury, Subhasish & Kovenock, Dan & Sheremeta, Roman, 2011. "An Experimental Investigation of Colonel Blotto Games," MPRA Paper 46810, University Library of Munich, Germany.
  4. Kovenock, D. & de Vries, C.G., 1995. "The All-Pay Auction with Complete Information," UFAE and IAE Working Papers 311.95, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
  6. Kovenock, Dan & Roberson, Brian, 2008. "Coalitional Colonel Blotto games with application to the economics of alliances
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    ," Discussion Papers, Research Unit: Market Processes and Governance SP II 2008-02, Social Science Research Center Berlin (WZB).
  7. 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.
  8. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  9. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
  10. 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.
  11. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-60, May.
  12. 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.
  13. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
  14. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  15. 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.
  16. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
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