Shapley Values and their Application Inside and Outside of Economics

Table of Contents

1. Between Efficiency and Fairness

2. Game Theory and Shapley Values

2.1. Introduction to Game Theory

2.1.1. Competitive Game Theory

2.1.2. Cooperative Game Theory

2.2. Solution Concept Shapley Values

2.2.1. Shapley Value axioms

2.2.2. The mathematical expression

2.2.3. Solution Examples

3. Application areas of Shapley Values

3.1. Profit- and Cost Allocation

3.1.1. Profit Allocation

3.1.2. Cost Allocation

3.1.3. Application evaluation

3.2. Applications in Marketing

3.2.1. Conversion Attribution

3.2.2. Product line optimization

3.2.3. Application evaluation

3.3. Applications in Machine Learning

3.3.1. Data valuation

3.3.2. Feature selection

3.3.3. Explainable Artificial Intelligence

3.3.4. Application evaluation

3.4. Further application areas

3.4.1. Applications in Politics

3.4.2. Applications in Portfolio Theory

3.4.3. Applications in Social Network Theory

3.4.4. Applications in Statistics

4. Conclusion

Research Objectives and Core Themes

This work aims to provide a holistic overview of application areas for the Shapley Value, a well-known concept in cooperative Game Theory used for fair payoff allocation. The primary objective is to categorize existing literature, analyze how the Shapley Value is employed in various fields, and evaluate its usefulness compared to alternative non-game theoretic methods, while identifying current trends and future relevance.

• Theoretical foundations of the Shapley Value and cooperative Game Theory.
• Applications in economic profit and cost allocation (e.g., transfer pricing, logistics).
• Employment in marketing for conversion attribution and product line selection.
• Use cases in machine learning, specifically data valuation, feature selection, and model explainability.
• Assessment of current research interest and future applicability in identified domains.

Excerpt from the Book

Summary of Chapters

1. Between Efficiency and Fairness: Introduces the economic problem of resource allocation and the necessity of allocation concepts that value fairness, leading to the introduction of the Shapley Value.

2. Game Theory and Shapley Values: Provides the theoretical grounding in competitive and cooperative Game Theory, detailing the mathematical definition and axiomatic basis of the Shapley Value.

3. Application areas of Shapley Values: Explores diverse practical implementations of the Shapley Value, ranging from profit/cost sharing to marketing analysis and machine learning optimization.

4. Conclusion: Synthesizes the main findings, discusses the research's contributions and limitations, and provides an outlook on future potential developments.

Keywords

Shapley Value, Cooperative Game Theory, Fair Allocation, Transfer Pricing, Cost Allocation, Conversion Attribution, Product Line Optimization, Data Valuation, Machine Learning, Feature Selection, Explainable Artificial Intelligence, XAI, Social Network Theory, Power Index, Portfolio Risk

Frequently Asked Questions

What is the primary focus of this work?

The research focuses on systematically categorizing and evaluating the diverse real-world application areas of the Shapley Value concept, originating from cooperative Game Theory.

What are the central thematic fields discussed?

The core themes include economic allocation (profit and cost), marketing analytics (attribution and product strategy), and technical fields like machine learning (data valuation and explainability).

What is the main objective of the thesis?

The objective is to provide a holistic overview of where the Shapley Value can be employed, how well it performs compared to other methods, and to estimate its future relevance in different sectors.

Which scientific method is utilized?

The work employs a comprehensive literature review approach, utilizing keyword-based searches across multiple academic databases to filter and analyze 168 unique relevant studies.

What does the main part cover?

The main part analyzes the Shapley Value's employment in transfer pricing, logistics transportation cost models, online marketing conversion attribution, and machine learning methodologies like SHAP.

Which keywords best characterize the work?

Key terms include Shapley Value, cooperative Game Theory, fair allocation, conversion attribution, data valuation, explainable AI, and cost allocation.

How is fairness defined within the context of the Shapley Value?

Fairness is interpreted through a set of predefined axioms—efficiency, symmetry, null player, and additivity—which define the Shapley Value's unique allocation mechanism.

What are the specific challenges of using Shapley Values in practice?

The primary challenges identified are its significant computational complexity and the difficulty of defining the underlying "worth function" for coalitions that may not exist in reality.