Handbook of the Shapley Value
Handbook of the Shapley Value

Author: Encarnación Algaba

Publisher: CRC Press

Published: 2019-12-06

Total Pages: 507

ISBN-13: 1351241397

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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.

Interpretable Machine Learning
Interpretable Machine Learning

Author: Christoph Molnar

Publisher: Lulu.com

Published: 2020

Total Pages: 320

ISBN-13: 0244768528

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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.

Handbook of Game Theory with Economic Applications
Handbook of Game Theory with Economic Applications

Author: R.J. Aumann

Publisher: Elsevier

Published: 1992

Total Pages: 824

ISBN-13: 9780444894274

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This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes

Models in Cooperative Game Theory
Models in Cooperative Game Theory

Author: Rodica Branzei

Publisher: Springer Science & Business Media

Published: 2008-03-08

Total Pages: 203

ISBN-13: 354077954X

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Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.

Fair Division and Collective Welfare
Fair Division and Collective Welfare

Author: Herve Moulin

Publisher: MIT Press

Published: 2004-08-20

Total Pages: 302

ISBN-13: 9780262633116

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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.

Contributions to the Theory of Games (AM-28), Volume II
Contributions to the Theory of Games (AM-28), Volume II

Author: Harold William Kuhn

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 408

ISBN-13: 1400881978

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These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.

The Shapley Value
The Shapley Value

Author: Alvin E. Roth

Publisher: Cambridge University Press

Published: 1988-10-28

Total Pages: 342

ISBN-13: 1107717213

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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.

Game Theory, Alive
Game Theory, Alive

Author: Anna R. Karlin

Publisher: American Mathematical Soc.

Published: 2017-04-27

Total Pages: 400

ISBN-13: 1470419823

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We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

Values of Non-Atomic Games
Values of Non-Atomic Games

Author: Robert J. Aumann

Publisher: Princeton University Press

Published: 2015-03-08

Total Pages: 348

ISBN-13: 1400867088

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The "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of non-atomic games, which are infinite-person games in which no individual player has significance. It is primarily a book of mathematics—a study of non-additive set functions and associated linear operators. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Strategies and Games, second edition
Strategies and Games, second edition

Author: Prajit K. Dutta

Publisher: MIT Press

Published: 2022-08-09

Total Pages: 713

ISBN-13: 0262046520

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The new edition of a widely used introduction to game theory and its applications, with a focus on economics, business, and politics. This widely used introduction to game theory is rigorous but accessible, unique in its balance between the theoretical and the practical, with examples and applications following almost every theory-driven chapter. In recent years, game theory has become an important methodological tool for all fields of social sciences, biology and computer science. This second edition of Strategies and Games not only takes into account new game theoretical concepts and applications such as bargaining and matching, it also provides an array of chapters on game theory applied to the political arena. New examples, case studies, and applications relevant to a wide range of behavioral disciplines are now included. The authors map out alternate pathways through the book for instructors in economics, business, and political science. The book contains four parts: strategic form games, extensive form games, asymmetric information games, and cooperative games and matching. Theoretical topics include dominance solutions, Nash equilibrium, Condorcet paradox, backward induction, subgame perfection, repeated and dynamic games, Bayes-Nash equilibrium, mechanism design, auction theory, signaling, the Shapley value, and stable matchings. Applications and case studies include OPEC, voting, poison pills, Treasury auctions, trade agreements, pork-barrel spending, climate change, bargaining and audience costs, markets for lemons, and school choice. Each chapter includes concept checks and tallies end-of-chapter problems. An appendix offers a thorough discussion of single-agent decision theory, which underpins game theory.