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Cake Cutting Algorithms Be Fair If You Can
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Book Synopsis Cake-Cutting Algorithms by : Jack Robertson
Download or read book Cake-Cutting Algorithms written by Jack Robertson and published by CRC Press. This book was released on 1998-07-15 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The challenge of dividing an asset fairly, from cakes to more important properties, is of great practical importance in many situations. Since the famous Polish school of mathematicians (Steinhaus, Banach, and Knaster) introduced and described algorithms for the fair division problem in the 1940s, the concept has been widely popularized. This book
Book Synopsis Cake-Cutting Algorithms by : Jack Robertson
Download or read book Cake-Cutting Algorithms written by Jack Robertson and published by A K Peters/CRC Press. This book was released on 1998-07-15 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The challenge of dividing an asset fairly, from cakes to more important properties, is of great practical importance in many situations. Since the famous Polish school of mathematicians (Steinhaus, Banach, and Knaster) introduced and described algorithms for the fair division problem in the 1940s, the concept has been widely popularized. This book gathers into one readable and inclusive source a comprehensive discussion of the state of the art in cake-cutting problems for both the novice and the professional. It offers a complete treatment of all cake-cutting algorithms under all the considered definitions of "fair" and presents them in a coherent, reader-friendly manner. Robertson and Webb have brought this elegant problem to life for both the bright high school student and the professional researcher.
Book Synopsis Cake-Cutting Algorithms-Be Fair If You Can by : Robertson&webb
Download or read book Cake-Cutting Algorithms-Be Fair If You Can written by Robertson&webb and published by Universities Press. This book was released on with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fair Division written by Steven J. Brams and published by Cambridge University Press. This book was released on 1996-02-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.
Book Synopsis Handbook of Computational Social Choice by : Felix Brandt
Download or read book Handbook of Computational Social Choice written by Felix Brandt and published by Cambridge University Press. This book was released on 2016-04-25 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.
Book Synopsis Economics and Computation by : Jörg Rothe
Download or read book Economics and Computation written by Jörg Rothe and published by Springer Nature. This book was released on 2024 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook connects three vibrant areas at the interface between economics and computer science: algorithmic game theory, computational social choice, and fair division. It thus offers an interdisciplinary treatment of collective decision making from an economic and computational perspective. Part I introduces to algorithmic game theory, focusing on both noncooperative and cooperative game theory. Part II introduces to computational social choice, focusing on both preference aggregation (voting) and judgment aggregation. Part III introduces to fair division, focusing on the division of both a single divisible resource ("cake-cutting") and multiple indivisible and unshareable resources ("multiagent resource allocation"). In all these parts, much weight is given to the algorithmic and complexity-theoretic aspects of problems arising in these areas, and the interconnections between the three parts are of central interest.
Book Synopsis Fair Division and Collective Welfare by : Herve Moulin
Download or read book Fair Division and Collective Welfare written by Herve Moulin and published by MIT Press. This book was released on 2004-08-20 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematics and Democracy by : Steven J. Brams
Download or read book Mathematics and Democracy written by Steven J. Brams and published by Princeton University Press. This book was released on 2009-12-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.
Book Synopsis Mathematical Snapshots by : H. Steinhaus
Download or read book Mathematical Snapshots written by H. Steinhaus and published by Courier Corporation. This book was released on 2012-07-12 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous photographs and diagrams explain mathematical phenomena in series of thought-provoking expositions. From simple puzzles to more advanced problems, topics include psychology of lottery players, new and larger prime numbers, and more. 391 illustrations.
Book Synopsis Algorithmic Game Theory by : Xiaotie Deng
Download or read book Algorithmic Game Theory written by Xiaotie Deng and published by Springer. This book was released on 2018-08-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Symposium on Algorithmic Game Theory, SAGT 2018, held in Beijing, China, in September 2018. The 19 full papers presented together with 6 short papers and 5 plenary talks were carefully reviewed and selected from 54 submissions. The papers cover various important aspects of algorithmic game theory including market equilibrium, auctions and applications, two sided markets, cake-cutting, cooperative games, voting games, multi-agent scheduling, price of stability, various mechanism design problems: online-dynamics and multi-stages as well as revenue maximization and resource allocation and applications.
Download or read book Math in Society written by David Lippman and published by . This book was released on 2012-09-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.
Book Synopsis Game Theory, Alive by : Anna R. Karlin
Download or read book Game Theory, Alive written by Anna R. Karlin and published by American Mathematical Soc.. This book was released on 2017-04-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis How to Think About Algorithms by : Jeff Edmonds
Download or read book How to Think About Algorithms written by Jeff Edmonds and published by Cambridge University Press. This book was released on 2008-05-19 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, for second- or third-year students of computer science, presents insights, notations, and analogies to help them describe and think about algorithms like an expert, without grinding through lots of formal proof. Solutions to many problems are provided to let students check their progress, while class-tested PowerPoint slides are on the web for anyone running the course. By looking at both the big picture and easy step-by-step methods for developing algorithms, the author guides students around the common pitfalls. He stresses paradigms such as loop invariants and recursion to unify a huge range of algorithms into a few meta-algorithms. The book fosters a deeper understanding of how and why each algorithm works. These insights are presented in a careful and clear way, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.
Book Synopsis The Geometry of Efficient Fair Division by : Julius B. Barbanel
Download or read book The Geometry of Efficient Fair Division written by Julius B. Barbanel and published by Cambridge University Press. This book was released on 2005-01-24 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the best way to divide a cake and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.
Download or read book STACS 2003 written by Helmut Alt and published by Springer Science & Business Media. This book was released on 2003-02-21 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2003, held in Berlin, Germany in February/March 2003. The 58 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 253 submissions. The papers address the whole range of theoretical computer science including algorithms and data structures, automata and formal languages, complexity theory, semantics, logic in computer science, as well as current challenges like biological computing, quantum computing, and mobile and net computing.
Book Synopsis Discourses on Social Software by : Jan van Eijck
Download or read book Discourses on Social Software written by Jan van Eijck and published by Amsterdam University Press. This book was released on 2009 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unusual format of a series of discussions among a logician, a computer scientist, a philosopher and some researchers from other disciplines encourages the reader to develop his own point of view. --Book Jacket.
Book Synopsis Albion's Seed by : David Hackett Fischer
Download or read book Albion's Seed written by David Hackett Fischer and published by Oxford University Press. This book was released on 1991-03-14 with total page 981 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating book is the first volume in a projected cultural history of the United States, from the earliest English settlements to our own time. It is a history of American folkways as they have changed through time, and it argues a thesis about the importance for the United States of having been British in its cultural origins. While most people in the United States today have no British ancestors, they have assimilated regional cultures which were created by British colonists, even while preserving ethnic identities at the same time. In this sense, nearly all Americans are "Albion's Seed," no matter what their ethnicity may be. The concluding section of this remarkable book explores the ways that regional cultures have continued to dominate national politics from 1789 to 1988, and still help to shape attitudes toward education, government, gender, and violence, on which differences between American regions are greater than between European nations.
