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

Jérôme Garnier-Brun (), Ruben Zakine () and Michael Benzaquen ()
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Jérôme Garnier-Brun: Università Bocconi
Ruben Zakine: LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Michael Benzaquen: LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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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 equilibriumlike 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 neighborhoodbased models [Phys. Rev. Lett. 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.

Date: 2025
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Published in Physical Review Letters, 2025, 135 (10), pp.107402. ⟨10.1103/3bj7-jc92⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05273341

DOI: 10.1103/3bj7-jc92

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