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Mean Field Games and Global Arms Races: Strategic Dynamics in a Multipolar World

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  • Heng-fu Zou

Abstract

This paper develops a dynamic game-theoretic framework to model global arms races in a multipolar world using mean field game (MFG) theory. We analyze the strategic behavior of a continuum of minor countries influenced by the military decisions of three major powers—the United States, China, and Russia — who engage in a finite-player differential game. Each country chooses its military expenditure over time to minimize a cost function that reflects internal costs and strategic positioning relative to others. We derive both general nonlinear and linear-quadratic-Gaussian (LQG) formulations, solve the coupled HJB–FPK systems, and simulate both time-dependent and stationary equilibria. Our results show how strategic interdependence, peer pressure, and deterrence incentives drive excessive militarization in decentralized equilibrium. We compare decentralized and centralized outcomes and analyze policy interventions such as caps and taxes. The framework offers a rigorous foundation for understanding military competition and evaluating arms control policies under uncertainty.

Suggested Citation

  • Heng-fu Zou, 2025. "Mean Field Games and Global Arms Races: Strategic Dynamics in a Multipolar World," CEMA Working Papers 756, China Economics and Management Academy, Central University of Finance and Economics.
    • Handle: RePEc:cuf:wpaper:756
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