IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v15y2025i3d10.1007_s13235-024-00577-4.html
   My bibliography  Save this article

On Stability of Nonlinear Armsbuilding Security Games

Author

Listed:
  • Jean Hénaff

    (CEA/DAM/Direction de l’Analyse Stratégique
    Univ. of Lille, Centrale Lille)

  • Jed Boufaied

    (Univ. of Lille, Centrale Lille)

  • Hélène Cadre

    (Univ. of Lille, Centrale Lille)

Abstract

We formulate a security game in a context of mixed armament acquisition, involving a finite set of Nations in strategic relationship, with utility functions which are nonlinear and non-differentiable on the boundary of their sets of definition. Since we want to study the long-term effect of the Nations’ investment in nuclear weapons, we focus on the steady-state analysis of the game. This requires us to extend the classical results from Rosen on compact-concave games, to unbounded concave games, relying on the uniform coercivity property of the Nations’ utility functions. In addition, we prove the existence and uniqueness, under mild assumptions, of an interior point Nash Equilibrium solution of the game. To learn the interior point Nash Equilibrium, we provide a decentralized proximal point-type algorithm, and derive a closed form expression of its convergence rate. Simulations are performed in case of a duopoly, illustrating the utility improvement and stabilizing effects of nuclear armaments, by comparison with the conventional-only setting. We subsequently generalize this result to an arbitrarily large, but finite, number of Nations. The problem is extended further by allowing arms trades between Nations, split into suppliers on the one side, and recipients—interpreted as opponents—on the other side. It is widely recognized that arms trades can have negative externalities on the international system’s security, and there are benefits to cooperate. Forming an export coalition enables the socialization of the operational costs among the coalition members and reallocation according to an ex-post cost allocation mechanism, while ensuring the maximization of the sum of the coalition members’ security functions. For a given coalition structure, we develop a partial equilibrium model of the international arms market. We prove the existence and uniqueness of a market equilibrium in arms trade prices and supply. Finally, we derive conditions on the exports, arms trade prices, and cost allocation mechanism guaranteeing the stability of the export coalition, thus highlighting the viability of a common defense policy for the export coalition.

Suggested Citation

  • Jean Hénaff & Jed Boufaied & Hélène Cadre, 2025. "On Stability of Nonlinear Armsbuilding Security Games," Dynamic Games and Applications, Springer, vol. 15(3), pages 729-768, July.
  • Handle: RePEc:spr:dyngam:v:15:y:2025:i:3:d:10.1007_s13235-024-00577-4
    DOI: 10.1007/s13235-024-00577-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-024-00577-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13235-024-00577-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:spr:dyngam:v:15:y:2025:i:3:d:10.1007_s13235-024-00577-4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.