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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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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Powell, Robert, 2006. "War as a Commitment Problem," International Organization, Cambridge University Press, vol. 60(1), pages 169-203, January.
    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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    More about this item

    Keywords

    Mean Field Games; Arms Race; Strategic Competition; Militarization; Linear-Quadratic-Gaussian Control; Decentralized Equilibrium;
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