Collective strategy condensation towards class-separated societies

TL;DR

This paper explores how envy-driven preferences in game theory can lead to the emergence of social classes through a collective strategy condensation transition, drawing an analogy to Bose-Einstein condensation in physics.

Contribution

It introduces a novel model linking envy in strategic interactions to the formation of social classes via a phase transition.

Findings

Envy induces a phase transition to class-separated societies.

Lower class members adopt identical strategies, akin to Bose-Einstein condensation.

Upper class members remain diverse and individualistic.

Abstract

In physics, the wavefunctions of bosonic particles collapse when the system undergoes a Bose-Einstein condensation. In game theory, the strategy of an agent describes the probability to engage in a certain course of action. Strategies are expected to differ in competitive situations, namely when there is a penalty to do the same as somebody else. We study what happens when agents are interested how they fare not only in absolute terms, but also relative to others. This preference, denoted envy, is shown to induce the emergence of distinct social classes via a collective strategy condensation transition. Members of the lower class pursue identical strategies, in analogy to the Bose-Einstein condensation, with the upper class remaining individualistic.