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

Area of Science:

• Active Matter Physics
• Collective Behavior Dynamics
• Agent-Based Modeling

Background:

• Self-interested agents lead to nonreciprocal interactions and out-of-equilibrium systems.
• Purely altruistic agents restore reciprocity and lead to equilibrium descriptions.

Purpose of the Study:

• Investigate how mixtures of self-interest and altruism affect macroscopic properties.
• Analyze the impact of altruism on system hydrodynamics and equilibrium.

Main Methods:

• Agent-based modeling of systems with self-interested and altruistic agents.
• Analysis of system hydrodynamics under varying fractions of altruists.
• Development of a well-mixed approximation for boundedly rational agents.
• Application of scalar field theory and active matter tools.

Main Results:

• A small fraction of altruists can suppress suboptimal clustering in highly rational systems.
• Altruists act as surfactants by localizing at interfaces.
• A well-mixed approximation simplifies the two-population model to a single effective field theory.
• Analytical characterization of altruism's effects on surface tension and nucleation dynamics.

Conclusions:

• Altruism can significantly alter the macroscopic behavior of agent systems.
• The surfactant-like behavior of altruists provides a mechanism for stabilizing systems.
• The developed theoretical framework allows for analytical predictions in complex agent dynamics.