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

TL;DR

This paper explores how cooperation and self-interest influence the collective behavior of agents, revealing that even a small amount of altruism can improve system efficiency and stability, with insights applicable to active matter physics.

Contribution

It introduces a two-population model combining selfish and altruistic agents, analyzing their macroscopic effects and applying active matter tools to bounded rationality scenarios.

Findings

Altruists act as surfactants at interfaces, reducing clustering.

Small fractions of altruists suppress sub-optimal clustering.

Analytical characterization of surface tension and nucleation dynamics.

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.