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Multi-battle contests over complementary battlefields

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  • Daniel Stephenson

    (Virginia Commonwealth University)

Abstract

This paper studies contests with complementary prizes where each agent simultaneously distributes a fixed budget over multiple battlefields. Each battlefield has a single prize which is divided among the competitors in proportion to an arbitrary power function of their investment levels. A unique pure strategy Nash equilibrium is shown to exist under arbitrarily sensitive battlefield success functions if objective functions exhibit constant subunitary elasticity of substitution between prize shares. In contrast, Blotto contests with linear objectives have only mixed strategy Nash equilibria if battlefield success functions are sufficiently sensitive to investment levels. Sufficient complementarity between prize shares allows pure strategy Nash equilibria to exist under arbitrarily sensitive battlefield success functions.

Suggested Citation

  • Daniel Stephenson, 2025. "Multi-battle contests over complementary battlefields," Review of Economic Design, Springer;Society for Economic Design, vol. 29(3), pages 659-674, September.
    • Handle: RePEc:spr:reecde:v:29:y:2025:i:3:d:10.1007_s10058-024-00351-3
    DOI: 10.1007/s10058-024-00351-3
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D4 - Microeconomics - - Market Structure, Pricing, and Design

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