BCAT — Bounded Confidence and Adoption Threshold Model

A mixed opinion dynamics and innovation diffusion simulation model for exploring the "best game no one played" phenomenon.

Companion Manuscript Repository

The manuscript source files, figures, and supporting information for the accompanying PLOS ONE paper are hosted separately:

• Manuscript Repository: github.com/canslab1/PLOS-BCAT

Overview

The BCAT (Bounded Confidence + Adoption Threshold) model integrates a bounded confidence-based opinion dynamics model with an adoption threshold innovation diffusion model. It simulates opinion exchanges and product acceptance behaviors across four types of theoretical social networks:

• Regular Lattice (CA): Toroidal 2D cellular automata with Moore neighborhood (rewiring probability = 0)
• Small-World Network (SWN): Watts-Strogatz model (0 < rewiring probability < 1)
• Random Network (RN): Fully rewired network (rewiring probability = 1)
• Scale-Free Network (SFN): Barabasi-Albert preferential attachment model

Each simulation consists of 400 agents connected by approximately 1,600 edges, with an average of 8 neighbors per agent.

Features

• Mixed model — Integrates bounded confidence opinion dynamics with adoption threshold innovation diffusion in a single simulation.
• Four network topologies — Regular Lattice (CA), Small-World (SWN), Random (RN), and Scale-Free (SFN) networks.
• Interactive GUI — Tkinter-based interface with real-time visualization of attitude trajectories, social networks, adoption dynamics, and distributions.
• Batch experiments — Run multiple repetitions with automatic result aggregation.
• Reproducible scenarios — Pre-configured parameter files for reproducing all key paper figures.
• Dual implementation — Both Python 3 (with GUI) and NetLogo 4.0.5 versions producing statistically equivalent results.

Installation

Python Version

• Python 3.10 or later (tested on Python 3.12 and 3.13)

Setup

git clone https://github.com/canslab1/BCAT.git
cd BCAT
pip install -r requirements.txt

Dependencies

Install all required packages:

pip install -r requirements.txt

Or install individually:

pip install numpy>=1.24.0 networkx>=3.0 matplotlib>=3.7.0

Standard Library Modules (no installation needed)

tkinter, random, os, time, math, threading, pickle, warnings

NetLogo Version (for .nlogo file)

• NetLogo 4.0.5 or later (available at https://ccl.northwestern.edu/netlogo/)

Usage

Python Version

python3 BCAT.py

This launches the GUI application with:

• Left panel: Parameter sliders, control buttons, Social Network visualization, and monitors
  • Social Network with legend (red = adopter; green gradient = non-adopter attitude level)
  • Monitors: Critical (critical point tick), FRI (Favorable Review Index), GSI (Good Sales Index)
• Right panel: Real-time visualization plots (4 rows, all titles in blue bold)
  • Row 1: Attitude Distribution, Threshold Distribution, Degree Distribution
  • Row 2: Attitude Trajectory with density colorbar legend (full-width, grid lines)
  • Row 3: Adoption Dynamics (adopter vs. non-adopter counts, full-width, grid lines)
  • Row 4: New Adopter Dynamics (full-width, grid lines)

Controls

Button	Function
Setup	Initialize the network and agent population
Run	Execute a complete simulation run (max-time steps)
Run Once	Execute a single time step
Experiments	Run batch experiments (no-of-experiments repetitions)
Save	Save current model state
Load	Load a previously saved model state

NetLogo Version

1. Open English - best game no one played.nlogo in NetLogo 4.0.5+
2. Adjust parameters using the interface sliders
3. Click "Setup" to initialize, then "Run once" to execute

Model Parameters

Parameter	Range	Default	Description
no-of-pioneers	0 -- 100	5	Number of initial adopter agents
clustered-pioneers?	ON/OFF	ON	Whether pioneers are spatially clustered
bounded-confidence	0 -- 90	50	Attitude distance threshold for opinion exchange
convergence-rate	0.1 -- 1.0	0.1	Rate of attitude adjustment per exchange
avg-of-attitudes	10 -- 100	50	Mean of initial attitude distribution
std-of-attitudes	0 -- 30	10	Std. dev. of initial attitude distribution
avg-of-thresholds	10 -- 100	40	Mean of adoption threshold distribution
std-of-thresholds	0 -- 30	10	Std. dev. of adoption threshold distribution
network-type	SFN / SWN	SWN/RN/CA	Social network topology
rewiring-probability	0.00 -- 1.00	0.00	Network rewiring probability (SWN only)
max-time	50 -- 1000	300	Maximum simulation time steps
no-of-experiments	10 -- 1000	20	Number of batch experiment repetitions

Reproducing Paper Results

Parameter configuration files for reproducing the simulation scenarios presented in the paper are provided in the test_scenarios/ directory.

Scenario 1: Favorable Review + Good Sales (Fig. 4)

python3 BCAT.py

Then set parameters: no-of-pioneers=5, clustered-pioneers=ON, bounded-confidence=50, convergence-rate=0.1, avg-of-attitudes=50, std-of-attitudes=10, avg-of-thresholds=20, std-of-thresholds=5, network-type=SWN/RN/CA, rewiring-probability=0.00, max-time=300. Click Setup, then Run.

Scenario 2: Downward Compatibility -- Opinion Dynamics Only (Fig. 11)

Set: avg-of-thresholds=100, std-of-thresholds=0, no-of-pioneers=0, bounded-confidence=10, convergence-rate=0.4, avg-of-attitudes=50, std-of-attitudes=20, network-type=SWN/RN/CA, rewiring-probability=0.00, max-time=300.

Scenario 3: Downward Compatibility -- Adoption Threshold Only (Fig. 12)

Set: avg-of-attitudes=100, std-of-attitudes=0, bounded-confidence=0, avg-of-thresholds=20, std-of-thresholds=10, no-of-pioneers=3, network-type=SWN/RN/CA, rewiring-probability=0.00, max-time=50.

Model Algorithm

The BCAT model operates in the following phases per time step:

1. Agent Selection: All agents are processed in random order each tick.
2. Neighbor Selection: Each agent randomly selects one neighboring agent.
3. Opinion Exchange: If the attitude difference is below the bounded confidence threshold, attitudes are adjusted according to four scenarios based on adoption status (see Algorithm 3 in the paper).
4. Adoption Decision: A not-yet-adopted agent with a positive attitude (att > 50) adopts if the proportion of adopted neighbors exceeds its adoption threshold.

Implementation Notes

• The Python version faithfully replicates the NetLogo 4.0.5 implementation, including the sequential execution semantics of NetLogo's ask-concurrent (which processes agents in random order with immediate effect).
• int(v + 0.5) is used as an equivalent to NetLogo's round() for positive values.
• NumPy arrays replace NetLogo's turtles-own for performance optimization.
• NetworkX graphs replace NetLogo's native turtle/link network structure.
• Both versions produce statistically equivalent results under identical random seeds and parameter settings.
• Attitude Trajectory rendering optimization: scatter points are grouped by color into 15 fixed PathCollection objects and updated incrementally via set_offsets(), reducing draw_idle() artist traversal from O(T×K) to O(1).
• Dual-Figure architecture: Social Network is rendered on a separate matplotlib Figure embedded in the left panel, allowing the three time-series plots (Attitude Trajectory, Adoption Dynamics, New Adopter Dynamics) to share a full-width X axis (Time) in the right panel.
• Evaluation metrics: FRI (Favorable Review Index = agents with attitude > 50 / total agents) and GSI (Good Sales Index = adopters / total agents) update in real time, displayed to 4 decimal places.
• Chart legends: Attitude Trajectory includes a 15-color density colorbar; Social Network legend shows node color meanings (adopter, attitude levels) without overlapping the graph.
• Degree Distribution alignment: bars are centered on integer ticks using ax.bar() instead of ax.hist() for accurate visual correspondence.

Data

The data/ directory contains the simulation output data underlying the tables and figures in the accompanying paper. These files constitute the minimal dataset required for replication.

Sensitivity Analysis (data/sensitivity_analysis/)

Raw output from 1,000-run batch experiments across four network topologies, used to generate Table 3 and Figs 7–9 in the paper.

File	Network Topology	Format
sensitivity_analysis_regular_lattice.xlsx	Regular Lattice (CA)	Excel
sensitivity_analysis_small_world.xlsx	Small-World (SWN)	Excel
sensitivity_analysis_random.xlsx	Random (RN)	Excel
sensitivity_analysis_scale_free.xlsx	Scale-Free (SFN)	Excel

Each workbook contains per-run records of adoption outcomes (adopter counts, critical points) across systematic parameter sweeps of the five primary model parameters.

Mechanism Decomposition (data/mechanism_decomposition/)

Results from three controlled experiments designed to disentangle the opinion clustering channel and the coordination failure channel in the opinion–adoption gap (Fig 10 in the paper, 30,000 total simulation runs).

File	Experiment	Topology	Runs	Description
md_a_lattice.csv	MD-A	Regular Lattice	7,000	Coordination failure isolated (FRI = 1.0 by construction)
md_a_smallworld.csv	MD-A	Small-World	7,000	Coordination failure isolated (FRI = 1.0 by construction)
md_b_lattice.csv	MD-B	Regular Lattice	1,000	Opinion clustering isolated (no pioneers, GSI = 0)
md_b_smallworld.csv	MD-B	Small-World	1,000	Opinion clustering isolated (no pioneers, GSI = 0)
md_c_lattice.csv	MD-C	Regular Lattice	7,000	Full BCAT baseline (both channels active)
md_c_smallworld.csv	MD-C	Small-World	7,000	Full BCAT baseline (both channels active)

CSV columns: experiment (run index), fri (Favorable Review Index at t=300), gsi (Good Sales Index at t=300), adopters (final adopter count), N (population size), avg_of_thresholds (threshold parameter), experiment_id (MD-A/MD-B/MD-C), topology (lattice/smallworld).

Finite-Size Scaling (data/finite_size_scaling/)

Results from scaling experiments at N=400, 900, 1,600, and 2,500 agents, confirming that the "best game no one played" phenomenon and the dominance of avg-of-thresholds are robust to system size.

File	Description
finite_size_scaling_results.csv	Raw per-run results across all system sizes
summary_by_threshold_and_N.csv	Aggregated mean FRI/GSI by threshold and N

Scripts

The scripts/ directory contains Python scripts for reproducing the paper's analyses and figures:

Script	Purpose
reproduce_table2_figs.py	Reproduce Table 3 and Figs 7–9 from sensitivity analysis data
generate_table2_and_figs.py	Generate Table 3 values and figure images

| run_mechanism_decomposition.py | Run MD-A/B/C mechanism decomposition experiments | | finite_size_scaling.py | Run finite-size scaling experiments at N=900, 1,600, 2,500 |

Project Structure

BCAT/
├── BCAT.py                                # Python 3 implementation with GUI (Tkinter + matplotlib)
├── English - best game no one played.nlogo # NetLogo 4.0.5 implementation
├── requirements.txt                       # Python dependencies
├── pyproject.toml                         # Project metadata (PEP 621)
├── CITATION.cff                           # Citation metadata
├── CHANGELOG.md                           # Version history
├── CONTRIBUTING.md                        # Contribution guidelines
├── COMPLEXITY_ANALYSIS.md                 # Time/space complexity analysis
├── data/                                  # Simulation output data for paper replication
│   ├── sensitivity_analysis/              # 1,000-run batch results (4 network topologies)
│   ├── mechanism_decomposition/           # MD-A/B/C experiments (30,000 runs, CSV)
│   └── finite_size_scaling/               # Scaling experiments (N=400–2,500)
├── scripts/                               # Analysis and experiment scripts
│   ├── reproduce_table2_figs.py           # Reproduce Table 3 and Figs 7–9
│   ├── generate_table2_and_figs.py        # Generate Table 3 values and figures
│   ├── run_mechanism_decomposition.py     # Run MD-A/B/C experiments
│   └── finite_size_scaling.py             # Run finite-size scaling experiments
├── test_scenarios/                        # Parameter configs for paper reproduction
│   ├── fig4_favorable_review_good_sales.json
│   ├── fig5_favorable_review_poor_sales.json
│   ├── fig11_opinion_dynamics_only.json
│   ├── fig12_adoption_threshold_only.json
│   └── sensitivity_analysis_1000_runs.json
└── LICENSE                                # MIT License

Authors

• Chung-Yuan Huang (黃崇源) — Department of Computer Science and Information Engineering, Chang Gung University, Taiwan (gscott@mail.cgu.edu.tw)
• Sheng-Wen Wang (Corresponding author) — Department of Finance and Information, National Kaohsiung University of Science and Technology, Taiwan (swwang@nkust.edu.tw)

Citation

If you use this software in your research, please cite:

Huang, C.-Y., & Wang, S.-W. (2026). Exploring the "Best Game No One Played" Phenomenon Using A Mixed Opinion Dynamics and Innovation Diffusion Model. PLOS ONE. (forthcoming)

See CITATION.cff for machine-readable citation metadata.

References

1. Wang, S.-W., Huang, C.-Y., & Sun, C.-T. (2022). Multiagent Diffusion and Opinion Dynamics Model Interaction Effects on Controversial Products. IEEE Access, 10, 115252–115270. https://doi.org/10.1109/ACCESS.2022.3218719

License

This project is licensed under the MIT License. See LICENSE for details.