Modeling a Case of Herding Behavior in a Multi-Player Game

TL;DR

This paper analyzes herding behavior in a large-scale online social game, examining the conditions under which collective behavior emerges and persists as the number of players becomes very large.

Contribution

It provides a detailed mathematical analysis of herding phenomena in multi-player games, including conditions for meanfield measures and condensation effects.

Findings

Identifies conditions for the existence of meanfield-like measures.

Shows the occurrence of a condensation phenomenon in the system.

Analyzes the stationary regime in the thermodynamic limit.

Abstract

The system mentioned in the title belongs to the family of the so-called massively multi-player online social games (MMOSG). It features a scoring system for the elements of the game that is prone to herding effects. We analyze in detail its stationary regime in the thermodynamic limit, when the number of players tends to infinity. In particular, for some classes of input sequences and selection policies, we provide necessary and sufficient conditions for the existence of a complete meanfield-like measure, showing off an interesting condensation phenomenon.