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

We study the hydrodynamics of a system of agents that optimize either their individual utility (self-interest) or the collective welfare (cooperation). When agents act selfishly, their interactions are nonreciprocal, driving the system out of equilibrium; by contrast, purely altruistic dynamics restore reciprocity and yield an equilibrium 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 suboptimal 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. 120, 208301 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.208301]. 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.