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A lottery Blotto game with heterogeneous items of asymmetric valuations

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  • Kim, Geofferey Jiyun
  • Kim, Jerim
  • Kim, Bara

Abstract

We develop a multi-player lottery Blotto game in which each contested item can be valuated differently by involved agents and in which each contested item can be differently valuated from other contested items. We prove that the Blotto game with a finite number of agents has a Nash equilibrium. We characterize all Nash equilibria for the case of two agents.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecolet:v:173:y:2018:i:c:p:1-5
    DOI: 10.1016/j.econlet.2018.09.001
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    References listed on IDEAS

    as
    1. 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.
    2. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    3. 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.
    4. Powell, Robert, 2009. "Sequential, nonzero-sum "Blotto": Allocating defensive resources prior to attack," Games and Economic Behavior, Elsevier, vol. 67(2), pages 611-615, November.
    5. Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
    6. Duffy, John & Matros, Alexander, 2015. "Stochastic asymmetric Blotto games: Some new results," Economics Letters, Elsevier, vol. 134(C), pages 4-8.
    7. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    8. Osorio, Antonio, 2013. "The lottery Blotto game," Economics Letters, Elsevier, vol. 120(2), pages 164-166.
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    Cited by:

    1. David Iliaev & Sigal Oren & Ella Segev, 2023. "A Tullock-contest-based approach for cyber security investments," Annals of Operations Research, Springer, vol. 320(1), pages 61-84, January.
    2. 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).
    3. 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.

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    More about this item

    Keywords

    Lottery Blotto game; Heterogeneous items; Asymmetric valuations; Nash equilibria; Lagrange multiplier;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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