The Non-Constant-Sum Colonel Blotto Game

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The Non-Constant-Sum Colonel Blotto Game

Author Info

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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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number CESifo Working Paper No. 2378.

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

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Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September. [Downloadable!] (restricted)
Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer, vol. 36(3), pages 441-460, March. [Downloadable!] (restricted)
Other versions:
- Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics. [Downloadable!]
- Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series dp434, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics. [Downloadable!]
Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer, vol. 8(2), pages 291-305.
Other versions:
- Baye, Michael R. & Kovenock, Dan & Vries, Casper de, 1995. "The All-pay Auction with Complete Information," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich.
- 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).
- 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.
- Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "The All-Pay Auction With Complete Information," Purdue University Economics Working Papers 1007, Purdue University, Department of Economics.
- Baye, M.R. & Kovenock, D. & De Varies, C.G., 1990. "The All-Pay Auction With Complete Information," Papers 9051, Tilburg - Center for Economic Research.
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. [Downloadable!]

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Subhasish M. Chowdhury & Dan Kovenock J. & Roman M. Sheremeta, 2009. "An Experimental Investigation of Colonel Blotto Games," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]

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