Shapley Values and their Application Inside and Outside of Economics

Inhaltsverzeichnis (Table of Contents)

• Between Efficiency and Fairness
• Game Theory and Shapley Values
  • Introduction to Game Theory
    • Competitive Game Theory
    • Cooperative Game Theory
  • Solution Concept Shapley Values
    • Shapley Value axioms
    • The mathematical expression
    • Solution Examples
• Application areas of Shapley Values
  • Profit- and Cost Allocation
    • Profit Allocation
    • Cost Allocation
    • Application evaluation
  • Applications in Marketing
    • Conversion Attribution
    • Product line optimization
    • Application evaluation
  • Applications in Machine Learning
    • Data valuation
    • Feature selection
    • Explainable Artificial Intelligence
    • Application evaluation
  • Further application areas
    • Applications in Politics
    • Applications in Portfolio Theory
    • Applications in Social Network Theory
    • Applications in Statistics

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This literature review aims to identify and categorize the application areas of the Shapley Value, a solution concept in cooperative game theory, and to assess the current and future relevance of these applications. The review integrates existing literature to provide a comprehensive overview and compare the Shapley Value's usefulness to other non-game theoretic methods.

• Application areas of the Shapley Value across various fields.
• Assessment of the current and future relevance of Shapley Value applications.
• Comparison of the Shapley Value with alternative non-game theoretic methods.
• Analysis of methodological approaches to identifying and categorizing Shapley Value applications.
• Evaluation of the practical use and advancements in Shapley Value applications.

Zusammenfassung der Kapitel (Chapter Summaries)

Between Efficiency and Fairness: This introductory chapter sets the stage by exploring the fundamental tension between efficiency and fairness in resource allocation problems, framing the need for a solution concept like the Shapley Value. It lays the groundwork for understanding the core principles of fairness and the challenges inherent in achieving both efficient and equitable outcomes. The chapter likely introduces the concept of cooperative game theory and its relevance to the broader discussion.

Game Theory and Shapley Values: This chapter provides a detailed explanation of game theory, differentiating between competitive and cooperative game theory. It introduces the Shapley Value as a solution concept within cooperative game theory, explaining its axioms and mathematical formulation. Specific examples are used to illustrate the calculation and application of the Shapley Value. This chapter forms the theoretical foundation for understanding the subsequent application chapters.

Application areas of Shapley Values: This chapter serves as an overarching section encompassing diverse applications of the Shapley Value. It synthesizes findings across various domains, including profit and cost allocation, marketing, machine learning, politics, portfolio theory, social network theory, and statistics. The chapter likely analyses the methods used to identify and categorize these application areas, and critically evaluates the use and future relevance of each.

Profit- and Cost Allocation: This chapter explores the use of the Shapley Value in profit and cost allocation problems. It likely examines different scenarios, models, and methodologies for applying the Shapley Value in this context, and possibly compares its performance with traditional methods. The chapter's discussion likely emphasizes how the Shapley Value addresses fairness concerns in resource distribution. Detailed examples from real-world applications are presented to illustrate the practical implications.

Applications in Marketing: This chapter focuses on the application of the Shapley Value in marketing contexts such as conversion attribution and product line optimization. It delves into how the Shapley Value helps to fairly allocate credit for marketing campaigns and optimize product portfolios. It likely details specific marketing models and analytical techniques where the Shapley Value plays a critical role, contrasting it with other standard marketing analytics approaches. The chapter aims to highlight the advantages of the Shapley Value in resolving complex attribution problems and improving decision-making in marketing.

Applications in Machine Learning: This chapter explores the emerging applications of the Shapley Value in machine learning, particularly in areas like data valuation, feature selection, and explainable AI. It likely investigates how the Shapley Value is used to quantify the contributions of individual data points or features to model performance, and facilitates understanding the reasoning behind machine learning predictions. The chapter provides examples of how the Shapley Value improves the interpretability and fairness of machine learning models. The relative advantages and limitations of the Shapley Value in these contexts are discussed.

Further application areas: This chapter examines applications of the Shapley Value in diverse fields such as politics, portfolio theory, social network theory, and statistics. The chapter likely explains how the Shapley Value is adapted and employed to address specific challenges and theoretical problems in these areas. The analysis assesses the unique contributions of the Shapley Value to each domain, highlighting its adaptability and widespread applicability across disciplines. It also explores the potential future directions for research and application of the Shapley Value in these diverse areas.

Schlüsselwörter (Keywords)

Shapley Value, Cooperative Game Theory, Fairness, Profit Allocation, Cost Allocation, Marketing, Conversion Attribution, Product Line Optimization, Machine Learning, Data Valuation, Feature Selection, Explainable AI, Politics, Portfolio Theory, Social Network Theory, Statistics, Application Areas, Literature Review.

Frequently Asked Questions: A Comprehensive Language Preview

What is the main topic of this literature review?

This literature review focuses on the Shapley Value, a solution concept in cooperative game theory, and its diverse applications across various fields. It aims to categorize these applications, assess their relevance, and compare the Shapley Value's effectiveness to alternative methods.

What are the key themes explored in this review?

Key themes include the application areas of the Shapley Value (profit/cost allocation, marketing, machine learning, politics, portfolio theory, social networks, statistics), the assessment of its current and future relevance, comparisons with non-game theoretic methods, analysis of methodological approaches to categorizing applications, and evaluation of practical use and advancements.

What is the Shapley Value, and why is it important?

The Shapley Value is a solution concept in cooperative game theory that provides a fair and efficient way to allocate resources or rewards among players who collaborate. Its importance lies in its ability to address fairness concerns in resource distribution and its adaptability across numerous domains.

Which application areas of the Shapley Value are covered in this review?

The review covers a wide range of applications, including profit and cost allocation, marketing (conversion attribution and product line optimization), machine learning (data valuation, feature selection, explainable AI), and further applications in politics, portfolio theory, social network theory, and statistics.

How does the Shapley Value apply to profit and cost allocation?

In profit and cost allocation, the Shapley Value helps to distribute profits or costs fairly among collaborating entities based on their contributions. It offers a more equitable alternative to traditional methods.

How is the Shapley Value used in marketing?

In marketing, the Shapley Value assists in resolving complex attribution problems by fairly allocating credit for marketing campaigns across various channels. It also aids in product line optimization.

What are the applications of the Shapley Value in machine learning?

In machine learning, the Shapley Value contributes to data valuation, feature selection, and explainable AI by quantifying the individual contributions of data points or features to model performance, thereby improving model interpretability and fairness.

What other areas explore the use of Shapley Values?

Beyond the areas mentioned above, the review also explores the applications and potential of the Shapley Value in politics, portfolio theory, social network analysis, and statistics, demonstrating its broad applicability across disciplines.

What is the overall structure of the literature review?

The review is structured into chapters covering: an introduction emphasizing the balance between efficiency and fairness; a detailed explanation of game theory and the Shapley Value; in-depth analyses of its applications in various fields; and finally, a summary and conclusion.

What are the key takeaways from this literature review?

The key takeaway is the versatility and growing importance of the Shapley Value as a solution concept for fair and efficient resource allocation across a wide range of disciplines. The review highlights its potential for addressing complex challenges and improving decision-making in various fields.

Where can I find more information on the Shapley Value?

This literature review provides a comprehensive overview, and further information can be found through the cited references within the full text (not included in this FAQ).