Envy in competitive societies induces a class-stratification transition

Societal structures are influenced by the interpersonal
behavior of their members, which includes the prosperity
to define oneself relative to other, denoted here `envy'. We
develop a game theoretical formulation which includes choice,
competition and envy [fn] C. Gros, Royal Society
Open Science, 7:200411, 2020.[/fn]. In a correspondence to interacting
classical particle the bare utility, choice, is equivalent
to a confining potential, competition to Coulomb repulsion
and envy to a self-consistent molecular field interaction.
Envy induces low reward agents to search for alternative
strategies, which runs out of phase space when envy reaches
a critical point. The spectrum of rewards (energy, in the
phsyics analogy), splits into two disjoint bands, which
correspond to a lower and an upper class. Extensive numerical
simmulation are presented together with a self-consitent
analytic treatment of class sperated state.