shapley-bankruptcy 0.1.1

Algorithms for computing the Shapley value in bankruptcy games

Shapley-Bankruptcy

Implementation of algorithms for computing the Shapley value in bankruptcy games. This repository contains implementations of algorithms proposed in the paper "On Computing the Shapley Value in Bankruptcy Games".

Overview

A bankruptcy game is a cooperative game where an estate of value E must be divided among creditors with claims w = (w₁, w₂, ..., wₙ). This implementation provides multiple efficient algorithms for computing the Shapley value in such games.

Installation

Requirements

• Python 3.11 or higher
• Poetry (for package management)

Setup

# Clone the repository
git clone <repository-url>
cd shapley-banckruptcy

# Install dependencies
poetry install

Usage

Basic Example

from algorithms import FastDPAlgorithm, MonteCarloAlgorithm, ExactSetAlgorithm

# Problem setup
E = 100  # Total estate value
w = [50, 60, 80]  # Claims of each player

# Select an algorithm and compute
algorithm = FastDPAlgorithm()
algorithm.compute(E, w)

# Get results
shapley_values = algorithm.return_value()
computation_time = algorithm.return_time()

print(f"Shapley values: {shapley_values}")
print(f"Computation time: {computation_time} seconds")

Implemented Algorithms

1. ExactSetAlgorithm

An exact algorithm based on the definition of the Shapley value. It enumerates all subsets to compute the value.

from algorithms import ExactSetAlgorithm

algorithm = ExactSetAlgorithm()
algorithm.compute(E, w)
result = algorithm.return_value()

Features:

• Guarantees exact results
• Time complexity: O(2ⁿ × n)
• Suitable for small-scale problems

2. FastDPAlgorithm

A fast algorithm using dynamic programming.

from algorithms import FastDPAlgorithm

algorithm = FastDPAlgorithm()
algorithm.compute(E, w)
result = algorithm.return_value()

Features:

• Efficient computation using dynamic programming
• Suitable for medium to large-scale problems

3. FastRecursiveAlgorithm

A fast algorithm using recursive formulas.

from algorithms import FastRecursiveAlgorithm

algorithm = FastRecursiveAlgorithm()
algorithm.compute(E, w)
result = algorithm.return_value()

Features:

• Fast computation using recursive formulas with memoization
• Optimized by precomputing characteristic functions

4. FastDualRecursiveAlgorithm

A fast algorithm using dual recursive formulas.

from algorithms import FastDualRecursiveAlgorithm

algorithm = FastDualRecursiveAlgorithm()
algorithm.compute(E, w)
result = algorithm.return_value()

Features:

• Recursive computation using dual characteristic functions
• Fast computation with memoization

5. MonteCarloAlgorithm

An approximation algorithm using the Monte Carlo method.

from algorithms import MonteCarloAlgorithm

# Specify the number of samples (default: 10000)
algorithm = MonteCarloAlgorithm(M=50000, seed=42)
algorithm.compute(E, w)
result = algorithm.return_value()

Features:

• Fast computation even for large-scale problems
• Adjustable balance between accuracy and speed via the number of samples M
• Reproducible results with seed setting

Output Rounding

All algorithms can round results to a specified number of decimal places (default: 5 digits).

algorithm = FastDPAlgorithm(round_digits=3)
algorithm.compute(E, w)
result = algorithm.return_value()  # Results rounded to 3 decimal places

Algorithm Details

For detailed descriptions and theoretical background of each algorithm, please refer to the paper "On Computing the Shapley Value in Bankruptcy Games".

Characteristic Function of Bankruptcy Games

The characteristic function v(S) of a bankruptcy game is defined as:

v(S) = max(0, E - Σ_{j∉S} wⱼ)

where E is the total estate value and wⱼ is the claim of player j.

Shapley Value

The Shapley value φᵢ for player i is defined as:

φᵢ = Σ_{S⊆N\{i}} (|S|!(n-|S|-1)!/n!) × [v(S∪{i}) - v(S)]

Performance

Choose an algorithm based on the problem size and accuracy requirements:

• Small-scale (n ≤ 10): ExactSetAlgorithm is appropriate
• Medium-scale (10 < n ≤ 20): FastDPAlgorithm or FastRecursiveAlgorithm is recommended
• Large-scale (n > 20): MonteCarloAlgorithm is practical

License

See the LICENSE file for license information.

Author

ShuntaYamazaki ([e-mail])

References

This is an implementation of algorithms proposed in the paper "On Computing the Shapley Value in Bankruptcy Games".