Market Microstructure Simulator

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Asset & Market

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Periods (T)

Asset lifespan. Each period: agents trade, then a stochastic dividend is paid. FV declines by E[d] each period (DLM §I p.1732)

E[dividend]

Expected per-period dividend. Each period pays 0 or 2×E[d] with equal probability. FV(0) = T×E[d] (DLM fn.5)

Agents (n)

Population size. Original experiment: n=6. Larger n → more liquid market, different α* threshold

Initial Cash

1000

Starting cash endowment per agent. Constrains maximum bid prices and total market liquidity

Init Shares

Starting shares per agent. Total supply = n × shares. Shares become worthless at period T (FV(T)=0)

Seed

PRNG seed for reproducibility. Controls dividend draws, risk coefficients, belief noise, and order shuffling

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Experience (α)

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Experienced %

33%

α = fraction who know FV(t) = (T−t)×E[d]. Higher α → faster bubble suppression. DLM found ⅓ experienced is sufficient to prevent bubbles (§II Table 2 p.1735). Experiment sweeps α from 0–100% to find the critical α*.

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Inexperienced Behavior

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Optimism Bias

30%

Upward shift in inexperienced agents' belief: belief = base × (1 + bias). Primary driver of bubble formation. Higher → larger price overshoot above FV

Noise

25%

Random belief dispersion among inexperienced agents. Higher → wider spread of individual valuations, more volatile prices

FV Anchoring

40%

Weight on initial FV(0) vs current FV(t): belief = FV(t)×(1−anchor) + FV(0)×anchor. High anchoring → agents slow to update, sustaining bubble longer

Momentum

20%

Trend-chasing strength: adds momentum×(P_t−P_t−1) to belief. Creates positive feedback loops. Higher → self-reinforcing bubble/crash dynamics

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Risk Preferences

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33%

34%

33%

Risk-Loving

33%

ρ ≈ 0.005. Low risk aversion → narrow spreads, aggressive bidding. Willing to overpay, fuels bubbles

Risk-Neutral

34%

ρ ≈ 0.020. Moderate spreads. Prices at expected value (DLM fn.5 assumes risk-neutrality for FV derivation)

Risk-Averse

33%

ρ ≈ 0.080. Wide spreads, conservative bids. CARA utility: U(W) = −exp(−ρW). Linked sliders always sum to 100%

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Communication

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Enable Strategic Talk

Pre-trade cheap-talk phase where agents send price signals. Enables the Comm Lounge building in Trading Floor animation

Lying Cost μ

c_l = cost of sending m ≠ θ (literal lie, Sobel 2020 Def. 3). Higher → more truthful price signals

Deception Cost μ

c_d = cost of belief manipulation D(m,θ) (Sobel 2020 Def. 4). Higher → less deceptive signals. See Choi et al. (2025) §5

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Experiment Grid

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n values

Comma-separated market sizes. Experiment finds α* for each n. Original experiment: n=6 (DLM §I p.1732)

Alpha steps

Resolution of α sweep: tests α = 0%, 5%, 10%, ... 100%. More steps → finer α* precision, slower

Replications

Monte Carlo replications per α value. Each uses a different seed. More reps → smoother curves, more robust α*

Threshold

0.15

Sweeps α from 0–100% for each (n, risk, knowledge) combo. Uses T, E[d], Seed from panels above.

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Risk Configs

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RL33 / RN34 / RA33 RL60 / RN20 / RA20 RL10 / RN20 / RA70

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Knowledge Configs

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Mild (bias=0.15) Moderate (bias=0.30) Severe (bias=0.50)

Fig. 1 — Price vs Fundamental Value

Note. Market clearing price (blue) against declining FV (green dashed). Volume as background bars. Core visualization from DLM (2005) Figure 1. Prices above FV indicate bubble; below indicate underpricing.

Fig. 2 — Bid-Ask Spread

Note. Best bid (green) and best ask (red) with shaded spread region. Purple dotted line shows absolute spread. Narrower spreads indicate better price discovery and higher liquidity.

Fig. 3 — P&L Distribution

Note. Final profit-and-loss histogram: experienced (blue) vs inexperienced (red). In bubble markets, experienced agents typically profit at inexperienced agents' expense (DLM §II p.1735).

Fig. 4 — Price Deviation from FV

Note. Per-period percentage deviation (P−FV)/FV. Red bars = overpricing (bubble), green = underpricing. Feeds into NAPD = Σ|P−FV|/(T×FV₀) metric (DLM §II p.1733–1734).

Fig. 5 — Belief Convergence

Note. Sampled agent belief trajectories. Experienced agents (solid) track FV; inexperienced (dotted) may diverge due to bias and anchoring. Convergence indicates information aggregation.

Fig. 6 — Trading Volume

Note. Number of executed trades per period. Higher volume in early periods reflects more disagreement about value. DLM §II p.1735 notes marginally significant turnover increase in mixed-experience markets.

Market Simulation Architecture

Complete pipeline from parameter configuration through CDA market simulation to α* analysis, based on Dufwenberg, Lindqvist & Moore (2005)

Edit in draw.io

Declining Fundamental Value

FV(t) = (T − t) × E[d]. The asset's intrinsic value declines linearly as remaining dividend periods decrease, reaching zero at period T.

FV(t) = (T − t) × E[d]

DLM (2005) §I p.1732, fn.5; Smith, Suchanek & Williams (1988)

Continuous Double Auction (CDA)

Market mechanism where agents submit limit orders (bids and asks). A trade executes whenever the highest bid meets or exceeds the lowest ask.

trade iff max(bid) ≥ min(ask)

DLM (2005) §I p.1732, fn.6; Smith (1962); Holt (1995)

Bubble Formation

Occurs when market price significantly and persistently exceeds fundamental value, driven by inexperienced agents' optimism bias and momentum chasing.

P(t) >> FV(t) for sustained t

DLM (2005) §II Fig.1 p.1733; Table 1 p.1734

α* — Critical Experience Threshold

The minimum fraction of experienced agents required to suppress bubble formation below a given NAPD threshold. Central result of this simulation.

α* = min{α : NAPD(α) < ε}

DLM (2005) §II Table 2 p.1735; §III p.1735–1736

CARA Utility

U(W) = −exp(−ρW). Constant Absolute Risk Aversion utility function. Parameter ρ determines risk attitude: ρ > 0 risk-averse, ρ = 0 neutral, ρ < 0 risk-loving.

U(W) = −exp(−ρ · W)

Standard CARA; cf. DLM (2005) fn.5 (risk-neutrality baseline)

Strategic Communication

Agents can send cheap-talk price signals before trading. Lying and deception costs (from Choi et al. 2025) determine signal credibility.

cost = c_l·|m−θ| + c_d·Δaction

Extension; cf. Choi et al. (2025)

Glossary & Reference

Key Terms

Term	Full Name	Description
CDA	Continuous Double Auction	Bilateral trading mechanism where multiple buyers and sellers submit orders simultaneously; matches occur when bid ≥ ask.
FV	Fundamental Value	Intrinsic asset value FV(t) = (T−t)×E[d], declining linearly to zero. Experienced agents track this; inexperienced may not.
NAPD	Normalized Absolute Price Deviation	Cumulative bubble measure: Σ\|P(t)−FV(t)\| / (T×FV₀). Higher values indicate larger, more sustained bubbles.
R²	Haessel R-squared	Goodness-of-fit: 1 − Σ(P−FV)²/Σ(P−P̄)². Values near 1 indicate prices track fundamental value closely.
Amp	Price Amplitude	max(P−FV)/FV₀ + \|min(P−FV)\|/FV₀. Total range of price deviation, capturing both bubble and crash.
α*	Alpha Star	Critical experienced fraction: α* = min{α : NAPD(α) < threshold}.
CARA	Constant Absolute Risk Aversion	Utility U(W) = −exp(−ρW). Risk pref ρ: positive = risk-averse, zero = neutral, negative = risk-loving.
Exp	Experienced Agent	Trader who knows FV and adjusts belief to track FV(t) = (T−t)×E[d] each period.
Inexp	Inexperienced Agent	First-time participant with optimism bias, anchoring, and momentum susceptibility — may overpay for the asset.
VWAP	Volume-Weighted Avg Price	Per-period average trade price weighted by volume: Σ(Pᵢ×Vᵢ)/ΣVᵢ.
E[d]	Dividend	Per-period stochastic payment drawn from distribution with mean E[d]. Paid to all shareholders each period.
Spread	Bid-Ask Spread	Difference between best ask and best bid. Wider spreads indicate lower liquidity.

Mathematical Notation

Expression	Meaning	Reference
FV(t) = (T−t) × E[d]	Fundamental value at period t; declines to 0 at T	DLM §I p.1732, fn.5
U(W) = −exp(−ρW)	CARA utility function with risk aversion ρ	Standard; DLM fn.5
NAPD = Σ\|P(t)−FV(t)\| / (T×FV₀)	Normalized absolute price deviation (bubble magnitude)	DLM §II p.1733–1734
α* = min{α : NAPD(α) < ε}	Critical experience fraction to suppress bubbles	DLM §II Table 2 p.1735
R² = 1 − Σ(P−FV)² / Σ(P−P̄)²	Haessel R-squared: price tracking quality	DLM §II p.1733; Haessel (1978)
Amp = max↑/FV₀ + \|min↓\|/FV₀	Price amplitude: total swing measure	DLM §II p.1734

Plot Descriptions

Price vs Fundamental Value

Market clearing price (blue line) against declining FV (green dashed). Volume shown as background bars. Core visualization from Dufwenberg et al. (2005) Figure 1.

Bid-Ask Spread

Best bid (green) and best ask (red) with shaded spread region. Purple dotted line shows absolute spread magnitude. Narrower spreads indicate better price discovery.

P&L Distribution

Histogram of final profit-and-loss: experienced agents (blue) vs inexperienced (red). In bubble markets, experienced agents typically profit at inexperienced agents' expense.

Price Deviation from FV

Per-period percentage deviation (P−FV)/FV. Red bars indicate overpricing (bubble), green bars indicate underpricing. Measures real-time bubble magnitude.

Belief Convergence

Sampled agent belief trajectories over time. Experienced agents (solid lines) track FV; inexperienced (dotted) may diverge significantly due to bias and anchoring.

Trading Volume

Number of executed trades per period. Optional: lies per period shown on secondary axis when strategic communication is enabled.

Experiment Charts

α Sweep Curve

NAPD (blue), amplitude (orange), and Haessel-R² (green) plotted against experienced fraction α. Red vertical line marks α* where NAPD crosses below threshold.

α* vs Market Size (n)

Main result chart: how the critical experience threshold α* varies with market size. Each line represents a (risk, knowledge) configuration. Key finding of the α* = f(n, risk, knowledge) analysis.

α* Heatmap

Risk composition × knowledge level matrix. Color intensity indicates α*: green (low) to red (high). Shows interaction effects between parameters.

α* vs Risk Composition

Grouped bar chart comparing α* across risk distributions for each knowledge level. Reveals how risk-loving populations affect bubble persistence.

Source Papers

Reference	Description
DLM (2005)	Dufwenberg, M., Lindqvist, T. & Moore, E. “Bubbles and Experience: An Experiment.” American Economic Review, 95(5), pp. 1731–1737. Core paper: shows ⅓ experienced traders sufficient to suppress bubbles in laboratory CDA markets.
SSW (1988)	Smith, V.L., Suchanek, G.L. & Williams, A.W. “Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets.” Econometrica, 56(5), pp. 1119–1151. Foundational paper on asset market bubbles with declining fundamental value.
Haessel (1978)	Haessel, W.W. “Measuring Goodness of Fit in Linear and Nonlinear Models.” Southern Economic Journal, 44(3), pp. 648–652. Defines Haessel-R² used to measure price-FV tracking quality.
King et al. (1993)	King, R.R., Smith, V.L., Williams, A.W. & Van Boening, M.V. “The Robustness of Bubbles and Crashes in Experimental Stock Markets.” In Chen, P. (ed.), Nonlinear Dynamics and Evolutionary Economics, pp. 183–200. Bubble measures: NAPD, amplitude.
Choi et al. (2025)	Choi, S., Lee, J. & Lim, W. (2025). Strategic communication with lying and deception costs. Defines augmented utility EU^a = material − c_l·lie − c_d·deception. Used in the Communication panel.
Smith (1962)	Smith, V.L. “An Experimental Study of Competitive Market Behavior.” Journal of Political Economy, 70(2), pp. 111–137. Pioneering work on CDA market mechanism.

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