The Shapley Value
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Interpretable Machine Learning
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Author : Christoph Molnar
language : en
Publisher: Lulu.com
Release Date : 2020
Interpretable Machine Learning written by Christoph Molnar and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Computers categories.
This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.
The Shapley Value
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Author : Alvin E. Roth
language : en
Publisher: Cambridge University Press
Release Date : 1988-10-28
The Shapley Value written by Alvin E. Roth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-28 with Business & Economics categories.
This volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper.
The Shapley Value
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Author : Alvin E. Roth
language : en
Publisher: Cambridge University Press
Release Date : 1988-10-28
The Shapley Value written by Alvin E. Roth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-28 with Business & Economics categories.
Composed in honour of the sixty-fifth birthday of Lloyd Shapley, this volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper. Each of the twenty essays concerns some aspect of the Shapley value. Three of the chapters are reprints of the 'ancestral' papers: Chapter 2 is Shapley's original 1953 paper defining the value; Chapter 3 is the 1954 paper by Shapley and Shubik applying the value to voting models; and chapter 19 is Shapley's 1969 paper defining a value for games without transferable utility. The other seventeen chapters were contributed especially for this volume. The first chapter introduces the subject and the other essays in the volume, and contains a brief account of a few of Shapley's other major contributions to game theory. The other chapters cover the reformulations, interpretations and generalizations that have been inspired by the Shapley value, and its applications to the study of coalition formulation, to the organization of large markets, to problems of cost allocation, and to the study of games in which utility is not transferable.
Handbook Of The Shapley Value
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Author : Encarnación Algaba
language : en
Publisher: CRC Press
Release Date : 2019-12-06
Handbook Of The Shapley Value written by Encarnación Algaba and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Business & Economics categories.
Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory. Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation." Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.
Modeling Computation And Optimization
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Author : S. K. Neogy
language : en
Publisher: World Scientific
Release Date : 2009
Modeling Computation And Optimization written by S. K. Neogy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume provides recent developments and a state-of-the-art review in various areas of mathematical modeling, computation and optimization. It contains theory, computation as well as the applications of several mathematical models to problems in statistics, games, optimization and economics for decision making. It focuses on exciting areas like models for wireless networks, models of Nash networks, dynamic models of advertising, application of reliability models in economics, support vector machines, optimization, complementarity modeling and games.
Cooperative Game Theory And Applications
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Author : Imma Curiel
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03-31
Cooperative Game Theory And Applications written by Imma Curiel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-31 with Business & Economics categories.
In this book applications of cooperative game theory that arise from combinatorial optimization problems are described. It is well known that the mathematical modeling of various real-world decision-making situations gives rise to combinatorial optimization problems. For situations where more than one decision-maker is involved classical combinatorial optimization theory does not suffice and it is here that cooperative game theory can make an important contribution. If a group of decision-makers decide to undertake a project together in order to increase the total revenue or decrease the total costs, they face two problems. The first one is how to execute the project in an optimal way so as to increase revenue. The second one is how to divide the revenue attained among the participants. It is with this second problem that cooperative game theory can help. The solution concepts from cooperative game theory can be applied to arrive at revenue allocation schemes. In this book the type of problems described above are examined. Although the choice of topics is application-driven, it also discusses theoretical questions that arise from the situations that are studied. For all the games described attention will be paid to the appropriateness of several game-theoretic solution concepts in the particular contexts that are considered. The computation complexity of the game-theoretic solution concepts in the situation at hand will also be considered.
Networks And Groups
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Author : Professor Bhaskar Dutta
language : en
Publisher:
Release Date : 2002-11-26
Networks And Groups written by Professor Bhaskar Dutta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-26 with categories.
The organization of individuals into networks and groups is of fundamental importance in many social and economic interactions. Examples range from networks of personal contacts used to obtain information about job opportunities to the formation of trading partnerships, alliances, cartels, and federations. Much of our understanding of how and why such networks and groups form, and the precise way in which the network or groups structure affects outcomes of social and economic interaction, is relatively new. This volume collects some of the central papers in this recent literature, which have made important progress on this topic.
Fair Division And Collective Welfare
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Author : Herve Moulin
language : en
Publisher: MIT Press
Release Date : 2004-08-20
Fair Division And Collective Welfare written by Herve Moulin and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-20 with Business & Economics categories.
The concept of fair division is as old as civil society itself. Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare. The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method. The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.
Shapley Values And Their Application Inside And Outside Of Economics
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Author :
language : en
Publisher: GRIN Verlag
Release Date : 2023-01-18
Shapley Values And Their Application Inside And Outside Of Economics written by and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-18 with Business & Economics categories.
Bachelor Thesis from the year 2022 in the subject Business economics - Business Management, Corporate Governance, grade: 1.15, Technical University of Ilmenau, language: English, abstract: The Shapley Value is a famous solution concept of cooperative Game Theory which aims at allocating a jointly generated payoff to the contributing members under fair circumstances. It represents a unique solution to a set of predefined fairness axioms which favoured its employment in many applications and scientific literature over the years. The resulting vast amount of literature is mainly focused on applying the Shapley Value in various areas, which created a discrepancy between the advancements in practical solutions and review sources which capture a holistic overview of possible application areas. The objectives of this literature review were therefore to firstly identify application areas, then highlight the respective employment and current advancements by integrating literature sources in a second step in order to discuss the usefulness in regard to popular non-game theoretic methods at the end. Methodically, a literature review was accomplished which utilized multiple databases and search-engines to find Shapley Value-related literature, which was used to categorize application areas. From there on, keyword- and forward/backward searches were executed for every identified application area to further enrich the literature basis. In total, 168 unique studies contributed to this review which revealed that Shapley Values are employed in Profit and Cost allocation, Marketing, Machine Learning, Politics, Portfolio and Social Network Theory and in Statistics. As this review also assessed the current and future relevance of individual application areas, it was projected that a majority of the here presented applications will be of value in the future.