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

Author

Listed:
  • 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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    References listed on IDEAS

    as
    1. Zou, Heng-fu, 1995. "A dynamic model of capital and arms accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 371-393.
    2. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    3. Powell, Robert, 2006. "War as a Commitment Problem," International Organization, Cambridge University Press, vol. 60(1), pages 169-203, January.
    4. Heng-Fu Zou, 1997. "Dynamic analysis in the Viner model of mercantilism," Journal of International Money and Finance, Elsevier, vol. 16(4), pages 637-651, August.
    5. Gong, Liutang & Zou, Heng-fu, 2003. "Military spending and stochastic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 153-170, October.
    6. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    7. Fearon, James D., 1995. "Rationalist explanations for war," International Organization, Cambridge University Press, vol. 49(3), pages 379-414, July.
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    Keywords

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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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