IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v125y2023icp94-100.html
   My bibliography  Save this article

Proportional resource allocation in dynamic n-player Blotto games

Author

Listed:
  • Anbarci, Nejat
  • Cingiz, Kutay
  • Ismail, Mehmet S.

Abstract

In this note, we introduce a general model of dynamic n-player multi-battle Blotto contests in which asymmetric resources and non-homogeneous battlefield prizes are possible. Each player’s probability of winning the prize in a battlefield is governed by a ratio-form contest success function and players’ resource allocation on that battlefield. We show that there exists a pure subgame perfect equilibrium in which players allocate their resources in proportion to the battlefield prizes for every history. We also give a sufficient condition that if there are two players and the contest success function is of Tullock type, then the subgame perfect equilibrium is unique.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:125:y:2023:i:c:p:94-100
    DOI: 10.1016/j.mathsocsci.2023.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489623000604
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2023.07.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kai A Konrad, 2018. "Budget and Effort Choice in Sequential Colonel Blotto Campaigns," CESifo Economic Studies, CESifo Group, vol. 64(4), pages 555-576.
    2. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    3. Dan Kovenock & Brian Roberson, 2009. "Is the 50-State Strategy Optimal?," Journal of Theoretical Politics, , vol. 21(2), pages 213-236, April.
    4. 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.
    5. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    6. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    7. Maria Montero & Alex Possajennikov & Martin Sefton & Theodore Turocy, 2016. "Majoritarian Blotto contests with asymmetric battlefields: an experiment on apex games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 55-89, January.
    8. Avidit Acharya & Takuo Sugaya & Eray Turkel, 2022. "Electoral Campaigns as Dynamic Contests," "Marco Fanno" Working Papers 0293, Dipartimento di Scienze Economiche "Marco Fanno".
    9. Duffy, John & Matros, Alexander, 2017. "Stochastic asymmetric Blotto games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 88-105.
    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. 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.
    12. 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.
    13. Dziubiński, Marcin & Goyal, Sanjeev & Minarsch, David E.N., 2021. "The strategy of conquest," Journal of Economic Theory, Elsevier, vol. 191(C).
    14. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    15. 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.
    16. Paulo Barelli & Srihari Govindan & Robert Wilson, 2014. "Competition for a Majority," Econometrica, Econometric Society, vol. 82(1), pages 271-314, January.
    17. Strumpf, Koleman S, 2002. "Strategic Competition in Sequential Election Contests," Public Choice, Springer, vol. 111(3-4), pages 377-397, June.
    18. 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.
    19. Yosef Rinott & Marco Scarsini & Yaming Yu, 2012. "A Colonel Blotto Gladiator Game," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 574-590, November.
    20. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    21. Hinnosaar, Toomas, 2024. "Optimal sequential contests," Theoretical Economics, Econometric Society, vol. 19(1), January.
    22. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    23. Kovenock, Dan & Rojo Arjona, David, 2019. "A full characterization of best-response functions in the lottery Colonel Blotto game," Economics Letters, Elsevier, vol. 182(C), pages 33-36.
    24. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
    25. Brams, Steven J. & Davis, Morton D., 1982. "Optimal resource allocation in presidential primaries," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 373-388, December.
    26. Duggan, John, 2007. "Equilibrium existence for zero-sum games and spatial models of elections," Games and Economic Behavior, Elsevier, vol. 60(1), pages 52-74, July.
    27. 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.
    28. 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.
    29. Duffy, John & Matros, Alexander, 2015. "Stochastic asymmetric Blotto games: Some new results," Economics Letters, Elsevier, vol. 134(C), pages 4-8.
    30. 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.
    31. Osorio, Antonio, 2013. "The lottery Blotto game," Economics Letters, Elsevier, vol. 120(2), pages 164-166.
    32. 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.
    33. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
    34. Christian Ewerhart & Julian Teichgräber, 2019. "Multi-battle contests, finite automata, and the tug-of-war," ECON - Working Papers 318, Department of Economics - University of Zurich.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    4. Kimbrough, Erik O. & Laughren, Kevin & Sheremeta, Roman, 2020. "War and conflict in economics: Theories, applications, and recent trends," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 998-1013.
    5. 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).
    6. 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.
    7. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    8. Shakun D. Mago & Roman M. Sheremeta, 2019. "New Hampshire Effect: behavior in sequential and simultaneous multi-battle contests," Experimental Economics, Springer;Economic Science Association, vol. 22(2), pages 325-349, June.
    9. Duffy, John & Matros, Alexander, 2017. "Stochastic asymmetric Blotto games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 88-105.
    10. 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.
    11. 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.
    12. 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.
    13. Shakun D. Mago & Roman M. Sheremeta, 2017. "Multi‐battle Contests: An Experimental Study," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 407-425, October.
    14. Deck, Cary & Hao, Li & Porter, David, 2015. "Do prediction markets aid defenders in a weak-link contest?," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 248-258.
    15. 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.
    16. Sebasti'an Morales & Charles Thraves, 2020. "On the Resource Allocation for Political Campaigns," Papers 2012.02856, arXiv.org.
    17. Nicolas Houy & Jean-Philippe Nicolaï & Marie Claire Villeval, 2020. "Always doing your best? Effort and performance in dynamic settings," Theory and Decision, Springer, vol. 89(3), pages 249-286, October.
    18. David Rietzke & Brian Roberson, 2013. "The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 937-956, April.
    19. Dan Kovenock & Brian Roberson, 2021. "Generalizations of the General Lotto and Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 997-1032, April.
    20. Xu, Jin & Zenou, Yves & Zhou, Junjie, 2022. "Equilibrium characterization and shock propagation in conflict networks," Journal of Economic Theory, Elsevier, vol. 206(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:125:y:2023:i:c:p:94-100. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.