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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.

Suggested Citation

  • Brian Roberson & Dmitriy Kvasov, 2010. "The Non-Constant-Sum Colonel Blotto Game," Purdue University Economics Working Papers 1252, Purdue University, Department of Economics.
  • Handle: RePEc:pur:prukra:1252
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    File URL: https://business.purdue.edu/research/Working-papers-series/2010/1252.pdf
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    References listed on IDEAS

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    1. 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, June.
    2. 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.
    3. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 833-861, April.
    4. 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.
    5. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    6. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    7. 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, August.
    8. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
    9. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    10. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
    11. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    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;Game Theory Society, vol. 41(2), pages 331-343, May.
    13. Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
    14. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    15. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-660, May.
    16. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
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    More about this item

    Keywords

    Colonel Blotto Game; All-Pay Auction; Contests; Mixed Strategies;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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