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

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  • Heng-Fu Zou

    (IAS, Wuhan University
    CEMA, Central University of Finance and Economics
    The World Bank)

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 re flects 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 equilib- rium. We compare decentralized and centralized outcomes and analyze policy interventions such as caps and taxes. The framework offers a rigorous foun dation 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," Annals of Economics and Finance, Society for AEF, vol. 26(2), pages 615-642, November.
    • Handle: RePEc:cuf:journl:y:2025:v:26:i:2:n:5:zou
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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • H56 - Public Economics - - National Government Expenditures and Related Policies - - - National Security and War
    • F51 - International Economics - - International Relations, National Security, and International Political Economy - - - International Conflicts; Negotiations; Sanctions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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