The Social Climbing Game

TL;DR

This paper models how individuals' desire for social status influences societal hierarchy formation, revealing a phase transition where increased social climbing leads to a strong hierarchy and reduced mobility.

Contribution

It introduces a stylized model demonstrating how social climbing incentives cause abrupt hierarchy formation and decreased mobility, highlighting a phase transition in societal structure.

Findings

Hierarchy strength increases sharply beyond a threshold of social climbing desire.

A well-defined hierarchy facilitates further climbing, reinforcing social order.

Higher social climbing incentives lead to ergodicity breaking and reduced mobility.

Abstract

The structure of a society depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society's hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined hierarchy allows agents to climb it, thus reinforcing it, whereas in a "disordered" society it is harder for agents to find out whom they should connect to in order to become more central. Interestingly, a social order emerges when agents strive harder to climb society and it results in a state of reduced social mobility, as a consequence of ergodicity breaking, where climbing is more difficult.