2009/11/30 by Dirk Helbing, Anders Johansson · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Psychology · Social Sciences · #Asymmetry #Biology #Computer science #Demography #Dynamics (music) #Econometrics #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Evolutionary biology #Evolutionary dynamics #Fluctuating asymmetry #Mathematics #Opinion Dynamics and Social Influence #Physics #Population #Power (physics) #Psychology #Sociology #Statistical physics #physics.comp-ph #physics.soc-ph #q-bio.PE
paper · pdf · doi:10.1103/physreve.81.016112
arxiv created 2010/01/04 · openalex publication_date 2010/01/26 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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"), (3) 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.