  Envy, the inclination to compare rewards, can be expected to unfold when
inequalities in terms of payoff differences are generated in competitive
societies. It is shown that increasing levels of envy lead inevitably to a
self-induced separation into a lower and an upper class. Class stratification
is Nash stable and strict, with members of the same class receiving identical
rewards. Upper class agents play exclusively pure strategies, all lower class
agents the same mixed strategy. The fraction of upper class agents decreases
progressively with larger levels of envy, until a single upper class agent is
left. Numerical simulations and a complete analytic treatment of a basic
reference model, the shopping trouble model, are presented. The properties of
the class-stratified society are universal and only indirectly controllable
through the underlying utility function, which implies that class stratified
societies are intrinsically resistant to political control. Implications for
human societies are discussed. It is pointed out that the repercussions of envy
are amplified when societies become increasingly competitive.
