Mean field model of a game for power

TL;DR

This paper models a power game as a dynamical system exhibiting positive feedback, analyzing fixed points to understand how power accumulates and stabilizes among players.

Contribution

It introduces a mean field dynamical model of power dynamics incorporating the Matthew effect, with analytical and numerical analysis of fixed points and stability.

Findings

Identification of fixed points and their stability

Insights into basins of attraction for power accumulation

Modeling of coercive power dynamics

Abstract

Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods allow to identify a set of fixed points of the model dynamics. The positions of the unstable fixed points give an insight on the basins of attraction of the stable fixed points. The results are interpreted in terms of modeling of coercive power.