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Generalizations of the General Lotto and Colonel Blotto Games

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  • Dan J. Kovenock
  • Brian Roberson

Abstract

In this paper, we generalize the General Lotto game and the Colonel Blotto game to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players, and for the players to have asymmetric resource constraints. We completely characterize Nash equilibrium in the generalized version of the General Lotto game and then show how this characterization can be applied to identify equilibria in the Colonel Blotto version of the game. In both games, we find that there exist sets of non-pathological parameter configurations of positive Lebesgue measure with multiple payoff nonequivalent equilibria.

Suggested Citation

  • Dan J. Kovenock & Brian Roberson, 2015. "Generalizations of the General Lotto and Colonel Blotto Games," CESifo Working Paper Series 5291, CESifo.
    • Handle: RePEc:ces:ceswps:_5291
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    2. Boyer, Pierre C. & Konrad, Kai A. & Roberson, Brian, 2017. "Targeted campaign competition, loyal voters, and supermajorities," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 49-62.
    3. Konrad, Kai A. & Morath, Florian, 2023. "How to preempt attacks in multi-front conflict with limited resources," European Journal of Operational Research, Elsevier, vol. 305(1), pages 493-500.
    4. Kjell Hausken, 2023. "Two-period Colonel Blotto contest with cumulative investments over variable assets with resource constraints," SN Business & Economics, Springer, vol. 3(11), pages 1-18, November.
    5. Ivan P. Yamshchikov & Sharwin Rezagholi, 2018. "Elephants, Donkeys, and Colonel Blotto," Papers 1805.12083, arXiv.org.
    6. Aner Sela, 2023. "Resource allocations in the best-of-k ( $$k=2,3$$ k = 2 , 3 ) contests," Journal of Economics, Springer, vol. 139(3), pages 235-260, August.
    7. Martin Gregor, 2021. "Electives Shopping, Grading Policies and Grading Competition," Economica, London School of Economics and Political Science, vol. 88(350), pages 364-398, April.
    8. Enric Boix-Adser`a & Benjamin L. Edelman & Siddhartha Jayanti, 2020. "The Multiplayer Colonel Blotto Game," Papers 2002.05240, arXiv.org, revised May 2021.
    9. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    10. 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).
    11. Ronald Peeters & Leonard Wolk, 2019. "Elicitation of expectations using Colonel Blotto," Experimental Economics, Springer;Economic Science Association, vol. 22(1), pages 268-288, March.
    12. Kostyantyn Mazur, 2017. "A Partial Solution to Continuous Blotto," Papers 1706.08479, arXiv.org, revised Sep 2017.
    13. Caroline Thomas, 2018. "N-dimensional Blotto game with heterogeneous battlefield values," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 509-544, May.
    14. 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.
    15. Marco Magnani, 2017. "Electoral competition with ideologically biased voters," Journal of Theoretical Politics, , vol. 29(3), pages 415-439, July.

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    More about this item

    Keywords

    Colonel Blotto game; General Lotto game; multi-battle contest; redistributive politics; all-pay auction;
    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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