Collective strategy condensation: When envy splits societies

TL;DR

This paper models how envy in societies with competitive options leads to spontaneous class stratification, with lower-class agents adopting identical strategies while upper-class agents act independently.

Contribution

It introduces a novel game-theoretic framework showing how envy causes endogenous class division through strategy condensation.

Findings

Lower-class agents adopt identical mixed strategies.

Upper-class agents follow individualist pure strategies.

Model results are consistent across large populations and confirmed by simulations.

Abstract

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.