IDEAS home Printed from https://ideas.repec.org/p/vcu/wpaper/2303.html
   My bibliography  Save this paper

Multi-battle contests over complementary battlefields

Author

Listed:
  • Daniel Graydon Stephenson

    (Department of Economics, VCU School of Business)

Abstract

This paper studies Blotto contests with divisible complementary prizes. Each agent distributes a fixed budget over multiple battlefields. Each battlefield has a single prize which is divided among the competi- tors in proportion to a power function of the corresponding investment levels. Prizes exhibit constant sub-unitary elasticity of substitution. Such contests are shown to have pure strategy Nash equilibria under arbitrarily sensitive battlefield success functions. In contrast, conven- tional Blotto and Tullock contests have no pure strategy Nash equi- libria under sufficiently sensitive battlefield success functions. These results suggest that divisible complementary prizes can help stabilize the distribution of resources in strategic conflicts.

Suggested Citation

  • Daniel Graydon Stephenson, 2023. "Multi-battle contests over complementary battlefields," Working Papers 2303, VCU School of Business, Department of Economics.
    • Handle: RePEc:vcu:wpaper:2303
    as

    Download full text from publisher

    File URL: https://danielgstephenson.com/items/ComplementaryBattlefieldsTheory.pdf
    File Function: First version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    2. Daron Acemoglu, 2002. "Directed Technical Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 781-809.
    3. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, vol. 100(4), pages 1330-1357, September.
    4. Hurwitz, Mark A & Caves, Richard E, 1988. "Persuasion or Information? Promotion and the Shares of Brand Name and Generic Pharmaceuticals," Journal of Law and Economics, University of Chicago Press, vol. 31(2), pages 299-320, 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. Anbarci, Nejat & Cingiz, Kutay & Ismail, Mehmet, 2018. "Multi-Battle n-Player Dynamic Contests," Research Memorandum 003, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. 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.
    8. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel Graydon Stephenson, 2023. "Convergence Rates in Resource Allocation Games," Working Papers 2304, VCU School of Business, Department of Economics.

    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. 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.
    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. 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.
    4. Dongya Koh & Raül Santaeulàlia-Llopis, 2017. "Countercyclical Elasticity of Substitution," Working Papers 946, Barcelona School of Economics.
    5. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    6. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    7. 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.
    8. Lawrence E. Blume & Steven N. Durlauf, 2015. "Capital in the Twenty-First Century: A Review Essay," Journal of Political Economy, University of Chicago Press, vol. 123(4), pages 749-777.
    9. Miguel A. Leon-Ledesma & Mathan Satchi, 2010. "A Note on Balanced Growth with a less than unitary Elasticity of Substitution," Studies in Economics 1007, School of Economics, University of Kent.
    10. Inoue, Emiko & Taniguchi, Hiroya & Yamada, Ken, 2022. "Measuring energy-saving technological change: International trends and differences," Journal of Environmental Economics and Management, Elsevier, vol. 115(C).
    11. Alvarez-Cuadrado, Francisco & Long, Ngo Van & Poschke, Markus, 2018. "Capital-labor substitution, structural change and the labor income share," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 206-231.
    12. Cristiano Cantore & Miguel León-Ledesma & Peter McAdam & Alpo Willman, 2014. "Shocking Stuff: Technology, Hours, And Factor Substitution," Journal of the European Economic Association, European Economic Association, vol. 12(1), pages 108-128, February.
    13. 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.
    14. Irit Nowik & Tahl Nowik, 2017. "Games with Costly Winnings," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-9, December.
    15. Cantore, C. & Ferroni, F. & León-Ledesma, M A., 2011. "Interpreting the Hours-Technology time-varying relationship," Working papers 351, Banque de France.
    16. Clemens Struck & Adnan Velic, 2017. "To Augment Or Not To Augment? A Conjecture On Asymmetric Technical Change," Trinity Economics Papers tep0117, Trinity College Dublin, Department of Economics.
    17. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    18. Osorio, Antonio, 2013. "The lottery Blotto game," Economics Letters, Elsevier, vol. 120(2), pages 164-166.
    19. Zha, Donglan & Kavuri, Anil Savio & Si, Songjian, 2018. "Energy-biased technical change in the Chinese industrial sector with CES production functions," Energy, Elsevier, vol. 148(C), pages 896-903.
    20. Michael Knoblach & Fabian Stöckl, 2020. "What Determines The Elasticity Of Substitution Between Capital And Labor? A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 847-875, September.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • Q34 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Natural Resources and Domestic and International Conflicts

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:vcu:wpaper:2303. 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: Oleg Korenok (email available below). General contact details of provider: https://edirc.repec.org/data/edvcuus.html .

    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.