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A Blotto Game with Multi-Dimensional Incomplete Information

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  • Dan Kovenock
  • Brian Roberson

Abstract

In the Colonel Blotto game, each of two players simultaneously allocates his fixed budget of a resource across a finite number n of battle elds. Within each battlefield, the player that allocates the higher level of the resource wins the battlefield. Each player's payoff is equal to the sum of the values of the battlefields he wins. In this paper we examine a multi-dimensional incomplete information version of the Colonel Blotto game in which each player's n-tuple of battlefield valuations is drawn from a common n-variate joint distribution function.

Suggested Citation

  • Dan Kovenock & Brian Roberson, 2010. "A Blotto Game with Multi-Dimensional Incomplete Information," Purdue University Economics Working Papers 1262, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1262
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    References listed on IDEAS

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    1. Yeon-Koo Che & Ian Gale, 1998. "Standard Auctions with Financially Constrained Bidders," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 1-21.
    2. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    3. 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.
    4. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
    5. Dan Kovenock & Brian Roberson, 2010. "Conflicts with Multiple Battlefields," Purdue University Economics Working Papers 1246, Purdue University, Department of Economics.
    6. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    7. Alexander Matros, 2007. "A Blotto Game with Incomplete Information," Working Paper 332, Department of Economics, University of Pittsburgh, revised Jul 2009.
    8. Adamo, Tim & Matros, Alexander, 2009. "A Blotto game with Incomplete Information," Economics Letters, Elsevier, vol. 105(1), pages 100-102, October.
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    Citations

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    Cited by:

    1. Duffy, John & Matros, Alexander, 2017. "Stochastic asymmetric Blotto games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 88-105.
    2. Christian Ewerhart & Dan Kovenock, 2019. "A Class of N-player Colonel Blotto games with multidimensional private information," ECON - Working Papers 336, Department of Economics - University of Zurich, revised Feb 2021.
    3. Denter, Philipp, 2020. "Campaign contests," European Economic Review, Elsevier, vol. 127(C).
    4. Sam Ganzfried, 2020. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Papers 2006.07443, arXiv.org, revised Jun 2021.
    5. Sam Ganzfried, 2021. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Games, MDPI, vol. 12(2), pages 1-11, June.
    6. Antoine Pietri, 2017. "Les modèles de « rivalité coercitive » dans l’analyse économique des conflits," Revue d'économie politique, Dalloz, vol. 127(3), pages 307-352.
    7. Nikoofal, Mohammad E. & Zhuang, Jun, 2015. "On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness," European Journal of Operational Research, Elsevier, vol. 246(1), pages 320-330.
    8. Kim, Jeongsim & Kim, Bara, 2017. "An asymmetric lottery Blotto game with a possible budget surplus and incomplete information," Economics Letters, Elsevier, vol. 152(C), pages 31-35.

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    More about this item

    Keywords

    Colonel Blotto Game; Con ict; Multi-dimensional Incomplete Information; Multi-dimensional Action Space;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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