README.md

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title: Limit Order Matching Microstructure
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Limit-Order-Matching-Microstructure

Paper: https://arxiv.org/abs/2511.20606
Code: https://github.com/Republic1024/Limit-Order-Matching-Microstructure

Unifying Matching Markets and Limit Order Books through Microstructure Dynamics

Code Release for: Limit Order Book Dynamics in Matching Markets: Microstructure, Spread, and Execution Slippage

📌 Overview

This repository contains the full simulation code, experiments, and visualization pipeline for the paper:

“Limit Order Book Dynamics in Matching Markets: Microstructure, Spread, and Execution Slippage”
arXiv: https://arxiv.org/abs/2511.20606

The project proposes a unified framework where matching markets (e.g., marriage, partner choice, labor matching) are modeled as limit order books, with:

• Intrinsic value → ask
• Reachability constraint → bid-depth / liquidity drought
• ΔV gap → structural spread
• Compensation C → imperfect price improvement
• Slippage (regret) → execution shortfall
• Settling → threshold-decay crossing event

The framework shows that linear compensation cannot close structural preference gaps, unless it triggers a categorical identity shift (Identity Collapse Threshold).

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🔍 Core Concepts

1. Unconditional vs. Reachable Maximum

• V_uncond_max: Best perceived partner that exists in the population.
• V_reach_max: Best partner currently reachable under social liquidity constraints.
• ΔV = V_uncond_max - V_reach_max:
  → The structural preference gap, analogous to a bid-ask spread.

2. Theorem 1 — Compensation Clipping & Identity Collapse

If compensation utility is:

h(C) = min(εC, C_max)

Then:

• If εC < C_max → Compensation is ineffective: ΔV persists
• If εC ≥ C_max → Identity Collapse: category shift occurs

This mirrors slippage-bounded execution in microstructure.

3. Threshold Dynamics (Settling)

Commitment occurs when:

θ = U_effective / V_uncond_max ≥ T(t)

Where T(t) is a decaying liquidity threshold (similar to urgency-driven execution).

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📁 Repository Structure

Limit-Order-Matching-Microstructure/
│
├── exp1-5.py               # Main experiments (Sections 4.2–4.6)
├── exp1-5-Chinese.py       # Chinese commented version
├── simulation_results.png  # Fig 5 replication
├── simulation_results2.png # Slippage + Clipping + Settling plots
├── data/                   # (Empty / Ignored) placeholder for datasets
├── img1.jpg                # Paper figure assets
├── img2.jpg
├── img3.jpg
├── .gitignore
└── README.md

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📊 Experiments Included (Sections 4.2–4.6)

Experiment 1 — Compensation Failure

Shows why compensation cannot close ΔV under clipping.

Experiment 2 — Settling Dynamics

Implements the threshold-decay commitment model.

Experiment 3 — Instant Commitment

High-tier reachable candidate → immediate match.

Experiment 4 — Regional Differences

Despite different compensation norms (Jiangsu vs Guangdong),
ranking is invariant → structural gaps dominate.

Experiment 5 — Regret Prediction

Shock to V_uncond_max yields post-match θ decline → slippage regret.

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🎨 Visualization

generate_academic_plots() reproduces Figures:

• Settling curve T(t) vs θ
• Compensation utility clipping (Theorem 1)
• Structural slippage bars

Outputs:

simulation_results2.png

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▶️ How to Run

1. Install dependencies

pip install numpy pandas matplotlib

2. Run the experiments

python exp1-5.py

3. Generate visualizations

(automatically triggered at the end)

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📚 Citation

If you use this framework, please cite:

Wu, Y. (2025). Limit Order Book Dynamics in Matching Markets:
Microstructure, Spread, and Execution Slippage.
arXiv:2511.20606.

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🧠 Philosophy Behind the Model (Short)

This project formalizes a fundamental principle:

Compensation cannot close structural gaps.
Only identity shifts can.

This emerges naturally from the microstructure mapping between
ΔV → spread,
C → bounded price improvement,
and slippage → structural regret.