Paper: arXiv 2508.17837

Authors: Matej Steinbacher, Mitja Steinbacher, Matjaz Steinbacher

Abstract

This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic bistability, which is not a result of randomness but an emergent property of micro-level trading rules, where even identical initial conditions lead to qualitatively different long-run price equilibria: a deterministic zero-price state and a persistent positive-price equilibrium. The study also identifies a metastable region with elevated volatility between the basins of attraction and reveals distinct transient behaviors for trajectories converging to these equilibria. Furthermore, we observe that the system is neither entirely regular nor fully chaotic. By highlighting the emergence of divergent market outcomes from uniform beginnings, this work contributes a novel perspective on the inherent path dependence and complex dynamics of artificial stock markets.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced nonlinear dynamics and bifurcation theory with HMM analysis, but relies entirely on simulated agent-based data with no real-market backtesting or statistical validation against historical data.

Research Flowchart

  flowchart TD
  A["Research Question: How do identical micro-trading rules in an artificial stock market lead to divergent macro-price dynamics?"] --> B["Methodology: Agent-Based Modeling<br>Endogenous Myopic Traders & Limit Order Book"]
  B --> C["Computational Process: Simulate identical initial conditions"]
  C --> D{"Outcome 1: Bimodal Equilibria"}
  C --> E{"Outcome 2: Metastable Volatility Region"}
  C --> F{"Outcome 3: Complex Dynamics<br>(Neither regular nor chaotic)"}
  D --> G["Key Finding: Intrinsic Path Dependence<br>Identical starts lead to<br>zero-price vs. positive-price states"]
  E --> G
  F --> G

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0 of 95 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.