Two Species Evolutionary Game Model of User and Moderator Dynamics

TL;DR

This paper models online communities with users and moderators using evolutionary game theory, analyzing stability and dynamics to explain community behaviors like Reddit's stability.

Contribution

It introduces a two-species evolutionary game model capturing interactions between users and moderators, providing explicit formulas for system stability and attraction basins.

Findings

System's long-term behavior depends on punishment level and moderator proportion.

Exact computation of the basin of attraction for optimal cooperation.

Identification of conditions leading to self-regulating community dynamics.

Abstract

We construct a two species evolutionary game model of an online society consisting of ordinary users and behavior enforcers (moderators). Among themselves, moderators play a coordination game choosing between being "positive" or "negative" (or harsh) while ordinary users play prisoner's dilemma. When interacting, moderators motivate good behavior (cooperation) among the users through punitive actions while the moderators themselves are encouraged or discouraged in their strategic choice by these interactions. We show the following results: (i) We show that the $\omega$-limit set of the proposed system is sensitive both to the degree of punishment and the proportion of moderators in closed form. (ii) We demonstrate that the basin of attraction for the Pareto optimal strategy $(\text{Cooperate},\text{Positive})$ can be computed exactly. (iii) We demonstrate that for certain initial conditions the system is self-regulating. These results partially explain the stability of many online users communities such as Reddit. We illustrate our results with examples from this online system.