IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2412.14996.html
   My bibliography  Save this paper

Hydrodynamics of Cooperation and Self-Interest in a Two-Population Occupation Model

Author

Listed:
  • Jerome Garnier-Brun
  • Ruben Zakine
  • Michael Benzaquen

Abstract

We study the hydrodynamics of a system of agents who optimize either their individual utility (self-interest) or the collective welfare (cooperation). When agents act selfishly, their interactions are non-reciprocal, driving the system out of equilibrium; by contrast, purely altruistic dynamics restore reciprocity and yield an equilibrium-like description. We investigate how mixtures of these two behaviors shape the macroscopic properties of the liquid of agents. For highly rational agents, we find that introducing a small fraction of altruists can suppress the sub-optimal clustering induced by selfish dynamics. This phenomenon can be attributed to altruists localizing at interfaces and acting as effective surfactants, shedding a new light on earlier findings in fixed neighborhood-based models [Phys. Rev. Lett. \textbf{120}, 208301 (2018)]. When agents are boundedly rational, we introduce a well-mixed approximation that reduces the two-population model to a single effective scalar field theory. This allows us to leverage state-of-the-art tools from active matter to analytically characterize how altruism modifies surface tension and nucleation dynamics.

Suggested Citation

  • Jerome Garnier-Brun & Ruben Zakine & Michael Benzaquen, 2024. "Hydrodynamics of Cooperation and Self-Interest in a Two-Population Occupation Model," Papers 2412.14996, arXiv.org, revised Aug 2025.
  • Handle: RePEc:arx:papers:2412.14996
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2412.14996
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    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:arx:papers:2412.14996. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.