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Multi-battle contests over complementary battlefields

Author

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  • 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
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    File URL: https://danielgstephenson.com/items/ComplementaryBattlefieldsTheory.pdf
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    References listed on IDEAS

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    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. 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).
    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. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    5. Daron Acemoglu, 2002. "Directed Technical Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 781-809.
    6. 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.
    7. 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.
    8. 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.
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    Cited by:

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

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    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

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