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The Lottery Blotto Game

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  • Osório Costa, Antonio Miguel

Abstract

In this paper we relax the Colonel Blotto game assumption that for a given battle the player who allocates the higher measure of resources wins that battle. We assume that for a given battle, the Colonel who allocates the higher measure of resources is more likely to win that battle. We have a simpler model for which we are able to compute all Nash equilibria in pure strategies for any valuations pro le that players might have. Something that is not possible for the original Blotto game. JEL: C72, D74, H56. KEYWORDS: Colonel Blotto game; lottery contest function.

Suggested Citation

  • Osório Costa, Antonio Miguel, 2013. "The Lottery Blotto Game," Working Papers 2072/211806, Universitat Rovira i Virgili, Department of Economics.
    • Handle: RePEc:urv:wpaper:2072/211806
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    References listed on IDEAS

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    1. Alex Robson, 2005. "Multi-Item Contests," ANU Working Papers in Economics and Econometrics 2005-446, Australian National University, College of Business and Economics, School of Economics.
    2. 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.
    3. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    4. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    5. 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.
    6. Dan Kovenock J. & Brian Roberson, 2010. "Conflicts with Multiple Battlefields," CESifo Working Paper Series 3165, CESifo.
    7. Alcalde, José & Dahm, Matthias, 2010. "Rent seeking and rent dissipation: A neutrality result," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 1-7, February.
    8. Caroline D. Thomas, 2009. "N-Dimensional Blotto Game with Asymmetric Battlefield Values," Department of Economics Working Papers 130116, The University of Texas at Austin, Department of Economics, revised Dec 2016.
    9. 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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    Cited by:

    1. Aymeric Vie, 2021. "A Genetic Algorithm approach to Asymmetrical Blotto Games with Heterogeneous Valuations," Papers 2103.14372, arXiv.org.
    2. Subhasish M Chowdhury & Dan Kovenock & David Rojo Arjona & Nathaniel T Wilcox, 2021. "Focality and Asymmetry in Multi-Battle Contests," The Economic Journal, Royal Economic Society, vol. 131(636), pages 1593-1619.
    3. Li, Xinmi & Zheng, Jie, 2022. "Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    4. Osório, António (António Miguel), 2018. "Conflict and Competition over Multi-Issues," Working Papers 2072/306550, Universitat Rovira i Virgili, Department of Economics.
    5. Sebasti'an Morales & Charles Thraves, 2020. "On the Resource Allocation for Political Campaigns," Papers 2012.02856, arXiv.org.
    6. Duffy, John & Matros, Alexander, 2015. "Stochastic asymmetric Blotto games: Some new results," Economics Letters, Elsevier, vol. 134(C), pages 4-8.
    7. Anbarci, Nejat & Cingiz, Kutay & Ismail, Mehmet S., 2023. "Proportional resource allocation in dynamic n-player Blotto games," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 94-100.
    8. Ivan P. Yamshchikov & Sharwin Rezagholi, 2018. "Elephants, Donkeys, and Colonel Blotto," Papers 1805.12083, arXiv.org.
    9. 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.
    10. Deutsch, Yael, 2021. "A polynomial-time method to compute all Nash equilibria solutions of a general two-person inspection game," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1036-1052.
    11. 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.
    12. Kim, Geofferey Jiyun & Kim, Jerim & Kim, Bara, 2018. "A lottery Blotto game with heterogeneous items of asymmetric valuations," Economics Letters, Elsevier, vol. 173(C), pages 1-5.
    13. Sebastián Morales & Charles Thraves, 2021. "On the Resource Allocation for Political Campaigns," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4140-4159, November.

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    More about this item

    Keywords

    Jocs no-cooperatius (Matemàtica); Gestió de conflictes; Seguretat nacional; 33 - Economia;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • H56 - Public Economics - - National Government Expenditures and Related Policies - - - National Security and War

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