Tullock Contest Solver

This project implements a solver for Tullock contests, computing Pure Nash Equilibrium (PNE) and ε-Approximate Nash Equilibrium (ε-NE) based on contest instances. The solver applies different algorithms based on the elasticity parameters of the contestants.

Features

• Computes PNE and ε-NE in Tullock contests.
• Handles different cases based on elasticity parameters (r values).
• Uses binary search and subset sum approximation techniques.
• Reads input from files and writes output to specified files.

Installation & Environment

Requirements

Ensure you have the following dependencies installed:

• Python 3.8+
• Required libraries:
  • numpy
  • scipy

Installation

Clone the repository and install dependencies:

git clone https://github.com/1653133307/Tullock.git
cd Tullock
pip install -r requirements.txt

Alternatively, install required libraries manually:

pip install numpy scipy

Usage

Run the Solver

You can run the solver by executing:

python Solver.py

Make sure your input file is in the correct format (see below).

Input Format

The input file should be a text file (**.txt**) with the following structure:

n
R
a_1 a_2 ... a_n
r_1 r_2 ... r_n

Where:

• n → Number of contestants (integer)
• R → Reward amount (float)
• a_1, a_2, ..., a_n → Efficiency parameters (list of floats)
• r_1, r_2, ..., r_n → Elasticity parameters (list of floats)

**Example Input (**input_sample_3.txt)

5
10
4.332009257737827 4.122455563544566 2.7494592222802523 4.262567021416704 4.053124274123181
1.9957465259789928 1.5590390196424875 1.8678656240993055 1.9391436075978281 1.9265985561604133

Output Format

The solver writes results to an output file. Each equilibrium solution is printed in the format:

Solution A_star: <A_star_value>
Player 1: Share = <share_1>, Effort = <effort_1>
Player 2: Share = <share_2>, Effort = <effort_2>
...

If no PNE exists, it returns:

No PNE

Example Output (output_sample_3.txt)

Processing file: input_sample_3.txt

No PNE exists

File Structure

Tullock/
│── Solver.py                  # Main script to run the solver
│── TullockContestSolver.py     # Core logic for computing equilibria
│── input_sample_1.txt          # Example input file
│── output_sample_1.txt         # Example output file
│── README.md                   # Documentation
│── requirements.txt            # Python dependencies

How It Works

1. The program reads input from a text file.
2. It initializes the TullockContestSolver with:
   • n: number of contestants
   • R: reward amount
   • a: efficiency parameters
   • r: elasticity parameters
3. Based on r values, it applies:
   • Algorithm 1 if all r ≤ 1
   • Algorithm 2 if allr ≤ 1 or r > 2
   • Algorithm 3 otherwise (ε-approximate Nash Equilibrium)
4. The solver computes the equilibrium solution and writes it to the output file.

License

This project is open-source under the MIT License.

Contact & Contributions

For questions or contributions, feel free to submit an issue or pull request on GitHub.

🚀 Happy Computing!