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Envy, the inclination to compare rewards, can be expected to unfold wheninequalities in terms of payoff differences are generated in competitivesocieties. It is shown that increasing levels of envy lead inevitably to aself-induced separation into a lower and an upper class. Class stratificationis Nash stable and strict, with members of the same class receiving identicalrewards. Upper class agents play exclusively pure strategies, all lower classagents the same mixed strategy. The fraction of upper class agents decreasesprogressively with larger levels of envy, until a single upper class agent isleft. Numerical simulations and a complete analytic treatment of a basicreference model, the shopping trouble model, are presented. The properties ofthe class-stratified society are universal and only indirectly controllablethrough the underlying utility function, which implies that class stratifiedsocieties are intrinsically resistant to political control. Implications forhuman societies are discussed. It is pointed out that the repercussions of envyare amplified when societies become increasingly competitive.

Self induced class stratification in competitive societies of agents: Nash stability in the presence of envy