Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power

TL;DR

This paper develops a mathematical framework to analyze the dynamics of heterogeneous populations with conflicting interactions, classifying system behaviors and phase transitions relevant to social, biological, and physical systems.

Contribution

It provides explicit formulas for stationary solutions and stability analysis in systems with two populations and conflicting interactions, considering asymmetry and power.

Findings

Classifies four types of system dynamics.

Identifies conditions for cooperation breakdown and coexistence.

Discusses phase transitions and polarization phenomena.

Abstract

Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified, and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (2) the evolution of commonly shared behaviors ("norms"), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics.