# Swarm behavior of traders with different subjective predictions in the Market

## TL;DR

This paper models trader swarm behavior in markets using a combination of queueing theory and mean field analysis, revealing how delays and market conditions influence collective trader dynamics.

## Contribution

It introduces a nonlinear Markov model that explains the emergence of swarm behavior driven by reaction delays and market states, independent of traders' subjective predictions.

## Key findings

- Swarm behavior arises from reaction delays and market conditions.
- Direction of swarm is influenced by market position and random behavior.
- Model explains collective trader dynamics without relying on subjective predictions.

## Abstract

A combination of a priority queueing model and mean field theory shows the emergence of traders' swarm behavior, even when each has a subjective prediction of the market driven by a limit order book. Using a nonlinear Markov model, we analyze the dynamics of traders who select a favorable order price taking into account the waiting cost incurred by others. We find swarm behavior emerges because of the delay in trader reactions to the market, and the direction of the swarm is decided by the current market position and the intensity of zero-intelligent random behavior, rather than subjective trader predictions.