IDEAS home Printed from https://ideas.repec.org/a/cuf/journl/y2025v26i2n5zou.html

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
    as

    Download full text from publisher

    File URL: http://down.aefweb.net/AefArticles/aef260205Zou.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Fearon, James D., 1995. "Rationalist explanations for war," International Organization, Cambridge University Press, vol. 49(3), pages 379-414, July.
    3. 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.
    4. Powell, Robert, 2006. "War as a Commitment Problem," International Organization, Cambridge University Press, vol. 60(1), pages 169-203, January.
    5. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Heng-fu Zou, 2025. "Power Accumulation and Endogenous Inequality: A Mean Field Game Approach to Elite Dominance," CEMA Working Papers 759, China Economics and Management Academy, Central University of Finance and Economics.
    2. Heng-fu Zou, 2025. "War, Capital, and the Birth of the State: A Mean Field Theory of Endogenous Political Dominance," CEMA Working Papers 754, China Economics and Management Academy, Central University of Finance and Economics.
    3. Heng-fu Zou, 2025. "Mean Field Games of Capital Accumulation and Militarization among Nations," CEMA Working Papers 755, China Economics and Management Academy, Central University of Finance and Economics.
    4. Heng-fu Zou, 2025. "The Rise of a Superpower: Endogenous Asymmetry in a Symmetric Mean Field Game of Militarization and Capital Accumulation," CEMA Working Papers 762, China Economics and Management Academy, Central University of Finance and Economics.
    5. Heng-fu Zou, 2025. "Militarization and Capital Accumulation: A Mean Field Game of Symmetric Nations under Strategic Externalities," CEMA Working Papers 761, China Economics and Management Academy, Central University of Finance and Economics.
    6. Wei Liang & Heng-fu Zou, 2026. "Militarization and Capital Accumulation: A Mean Field Game under Security Congestion," CEMA Working Papers 807, China Economics and Management Academy, Central University of Finance and Economics.
    7. Heng-fu Zou, 2025. "Tariff Wars and the Mercantilist-Nationalist Trap: A Mean Field Game of Strategic Trade and Global Finance," CEMA Working Papers 760, China Economics and Management Academy, Central University of Finance and Economics.
    8. Dmitriy Sergeyev & Chen Lian & Yuriy Gorodnichenko, 2023. "The Economics of Financial Stress," NBER Working Papers 31285, National Bureau of Economic Research, Inc.
    9. Chan, Kenneth S. & Laffargue, Jean-Pierre, 2016. "Plunder and tribute in a Malthusian world," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 138-150.
    10. Ricardo Alonzo Fern'andez Salguero, 2025. "SIMPOL Model for Solving Continuous-Time Heterogeneous Agent Problems," Papers 2509.23557, arXiv.org.
    11. Robert Brown, 2010. "Measuring Delegation," The Review of International Organizations, Springer, vol. 5(2), pages 141-175, June.
    12. Han, Jungsuk & Wang, Yenan, 2025. "All that glitters: A theory of multiple bubbles with implications for cryptocurrencies," Journal of Monetary Economics, Elsevier, vol. 152(C).
    13. Bonfatti, Roberto & O'Rourke, Kevin Hjortshøj, 2014. "Growth, Import Dependence and War," CEPR Discussion Papers 10073, C.E.P.R. Discussion Papers.
    14. Wagner, Matthew L, 2016. "The civil war puzzle revisited: The use of post-conflict elections as part of peace agreements," International Journal of Development and Conflict, Gokhale Institute of Politics and Economics, vol. 6(1), pages 1-24.
    15. John Tyson Chatagnier, 2015. "Conflict bargaining as a signal to third parties," Journal of Theoretical Politics, , vol. 27(2), pages 237-268, April.
    16. Vincenzo Bove & Ron Smith, 2011. "The Economics of Peacekeeping," Chapters, in: Derek L. Braddon & Keith Hartley (ed.), Handbook on the Economics of Conflict, chapter 10, Edward Elgar Publishing.
    17. Yukari Iwanami, 2024. "Asymmetric burden-sharing and the restraining and deterrence effects of alliances," Journal of Peace Research, Peace Research Institute Oslo, vol. 61(5), pages 711-725, September.
    18. Mathieu Couttenier & Sophie Hatte & Lucile Laugerette & Tommaso Sonno, 2025. "Dear Brothers and Sisters: Pope's Speeches and the Dynamics of Conflict in Africa," Working Papers hal-05029770, HAL.
    19. David R. Andersen-Rodgers, 2015. "No table necessary? Foreign policy crisis management techniques in non-state actor-triggered crises," Conflict Management and Peace Science, Peace Science Society (International), vol. 32(2), pages 200-221, April.
    20. Kazuhiro Obayashi, 2014. "Information, rebel organization and civil war escalation: The case of the Liberation Tigers of Tamil Eelam," International Area Studies Review, Center for International Area Studies, Hankuk University of Foreign Studies, vol. 17(1), pages 21-40, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cuf:journl:y:2025:v:26:i:2:n:5:zou. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.