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Proportional resource allocation in dynamic n-player Blotto games

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Listed:
  • Nejat Anbarc{i}
  • Kutay Cingiz
  • Mehmet S. Ismail

Abstract

A variety of social, economic, and political interactions have long been modelled after Blotto games. In this paper, we introduce a general model of dynamic $n$-player Blotto contests. The players have asymmetric resources, and the battlefield prizes are not necessarily homogeneous. Each player's probability of winning the prize in a battlefield is governed by a contest success function and players' resource allocation on that battlefield. We show that there exists a subgame perfect equilibrium in which players allocate their resources proportional to the battlefield prizes for every history. This result is robust to exogenous resource shocks throughout the game.

Suggested Citation

  • Nejat Anbarc{i} & Kutay Cingiz & Mehmet S. Ismail, 2020. "Proportional resource allocation in dynamic n-player Blotto games," Papers 2010.05087, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2010.05087
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    References listed on IDEAS

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    1. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    2. Kai A Konrad, 2018. "Budget and Effort Choice in Sequential Colonel Blotto Campaigns," CESifo Economic Studies, CESifo Group, vol. 64(4), pages 555-576.
    3. Brams, Steven J. & Davis, Morton D., 1974. "The 3/2's Rule in Presidential Campaigning," American Political Science Review, Cambridge University Press, vol. 68(1), pages 113-134, March.
    4. Brams, Steven J. & Davis, Morton D., 1982. "Optimal resource allocation in presidential primaries," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 373-388, December.
    5. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    6. Dan Kovenock & Brian Roberson, 2009. "Is the 50-State Strategy Optimal?," Journal of Theoretical Politics, , vol. 21(2), pages 213-236, April.
    7. Deck, Cary & Sheremeta, Roman, 2012. "Fight or Flight?," MPRA Paper 52130, University Library of Munich, Germany.
    8. Krueger, Anne O, 1974. "The Political Economy of the Rent-Seeking Society," American Economic Review, American Economic Association, vol. 64(3), pages 291-303, June.
    9. 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.
    10. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
    11. Qiang Fu & Jingfeng Lu & Yue Pan, 2015. "Team Contests with Multiple Pairwise Battles," American Economic Review, American Economic Association, vol. 105(7), pages 2120-2140, July.
    12. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    13. Duffy, John & Matros, Alexander, 2015. "Stochastic asymmetric Blotto games: Some new results," Economics Letters, Elsevier, vol. 134(C), pages 4-8.
    14. Duffy, John & Matros, Alexander, 2017. "Stochastic asymmetric Blotto games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 88-105.
    15. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
    16. Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 863-882, October.
    17. Harris, Christopher J & Vickers, John S, 1985. "Patent Races and the Persistence of Monopoly," Journal of Industrial Economics, Wiley Blackwell, vol. 33(4), pages 461-481, June.
    18. Deck, Cary & Sarangi, Sudipta & Wiser, Matt, 2017. "An experimental investigation of simultaneous multi-battle contests with strategic complementarities," Journal of Economic Psychology, Elsevier, vol. 63(C), pages 117-134.
    19. Dziubiński, Marcin & Goyal, Sanjeev & Minarsch, David E.N., 2021. "The strategy of conquest," Journal of Economic Theory, Elsevier, vol. 191(C).
    20. Arad, Ayala & Rubinstein, Ariel, 2012. "Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game," Journal of Economic Behavior & Organization, Elsevier, vol. 84(2), pages 571-585.
    21. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    22. Klumpp, Tilman & Konrad, Kai A. & Solomon, Adam, 2019. "The dynamics of majoritarian Blotto games," Games and Economic Behavior, Elsevier, vol. 117(C), pages 402-419.
    23. Strumpf, Koleman S, 2002. "Strategic Competition in Sequential Election Contests," Public Choice, Springer, vol. 111(3-4), pages 377-397, June.
    24. Yosef Rinott & Marco Scarsini & Yaming Yu, 2012. "A Colonel Blotto Gladiator Game," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 574-590, November.
    25. Hinnosaar, Toomas, 2024. "Optimal sequential contests," Theoretical Economics, Econometric Society, vol. 19(1), January.
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    1. 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.

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