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.

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)

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. 10)

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. 11)

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.

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
├── test_scenarios/                        # Parameter configs for paper reproduction
│   ├── fig4_favorable_review_good_sales.json
│   ├── fig5_favorable_review_poor_sales.json
│   ├── fig10_opinion_dynamics_only.json
│   ├── fig11_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. (2025). 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.