  Human societies are characterized, besides others, by three constituent
features. (A) Options, as for jobs and societal positions, differ with respect
to their associated monetary and non-monetary payoffs. (B) Competition leads to
reduced payoffs when individuals compete for the same option with others. (C)
People care how they are doing relatively to others. The latter trait, the
propensity to compare one's own success with that of others, expresses itself
as envy.
  It is shown that the combination of (A)-(C) leads to spontaneous class
stratification. Societies of agents split endogenously into two social classes,
an upper and a lower class, when envy becomes relevant. A comprehensive
analysis of the Nash equilibria characterizing a basic reference game is
presented. Class separation is due to the condensation of the strategies of
lower-class agents, which play an identical mixed strategy. Upper class agents
do not condense, following individualist pure strategies.
  Model and results are size-consistent, holding for arbitrary large numbers of
agents and options. Analytic results are confirmed by extensive numerical
simulations. An analogy to interacting confined classical particles is
discussed.
