Two Sided Matching

Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions.

Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets ... The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature.' From the Foreword by Robert Aumann

Matching problems with preferences are all around us OCo they arise when agents seek to be allocated to one another on the basis of ranked preferences over potential outcomes. Efficient algorithms are needed for producing matchings that optimise the satisfaction of the agents according to their preference lists.In recent years there has been a sharp increase in the study of algorithmic aspects of matching problems with preferences, partly reflecting the growing number of applications of these problems worldwide. This book describes the most important results in this area, providing a timely update to The Stable Marriage Problem: Structure and Algorithms (D Gusfield and R W Irving, MIT Press, 1989) in connection with stable matching problems, whilst also broadening the scope to include matching problems with preferences under a range of alternative optimality criteria."

This book probes the stable marriage problem and its variants as a rich source of problems and ideas that illustrate both the design and analysis of efficient algorithms. It covers the most recent structural and algorithmic work on stable matching problems, simplifies and unifies many earlier proofs, strengthens several earlier results, and presents new results and more efficient algorithms. The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a more general set of problems. The relationship between the structure of the stable marriage problem and the more general stable roommates problem is demonstrated, revealing many commonalities. The results the authors obtain provide an algorithmic response to the practical, and political, problems created by the asymmetry inherent in the Gale Shapley solutions, leading to alternative methods and better compromises than are provided by the Gale Shapley method. And, in contrast to Donald Knuth's earlier work which primarily focused on the application of mathematics to the analysis of algorithms, this book illustrates the productive and almost inseparable relationship between mathematical insight and the design of efficient algorithms. Dan Gusfield is Associate Professor of Computer Science at the University of California, Davis. Robert W. Irving is Senior Lecturer in Computing Science at the University of Glasgow. The Stable Marriage Problem is included in the Foundations of Computing Series, edited by Michael Garey and Albert Meyer.

The Social Cloud framework leverages existing relationships between members of a social network for the exchange of resources. This thesis focuses on the design of coordination mechanisms to address two challenges in this scenario. In the first part, user participation incentives are studied. In the second part, heuristics for two-sided matching-based resource allocation are designed and evaluated.

'This is a very stimulating book!' - N. G. de Bruijn. 'This short book will provide extremely enjoyable reading to anyone with an interest in discrete mathematics and algorithm design' - ""Mathematical Reviews"". 'This book is an excellent (and enjoyable) means of sketching a large area of computer science for specialists in other fields: It requires little previous knowledge, but expects of the reader a degree of mathematical facility and a willingness to participate. It is really neither a survey nor an introduction; rather, it is a paradigm, a fairly complete treatment of a single example used as a synopsis of a larger subject' - ""SIGACT News"". 'Anyone would enjoy reading this book. If one had to learn French first, it would be worth the effort!' - ""Computing Reviews"". The above citations are taken from reviews of the initial French version of this text - a series of seven expository lectures that were given at the University of Montreal in November of 1975.The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms. The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included.The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms. Donald E. Knuth is one of the most prominent figures of modern computer science. His works in ""The Art of Computer Programming"" are classic. He is also renowned for his development of TeX and METAFONT. In 1996, Knuth won the prestigious Kyoto Prize, considered to be the nearest equivalent to a Nobel Prize in computer science.

A broad overview of market mechanisms, with an emphasis on the interplay between theory and real-life applications; examples range from eBay auctions to school choice. This book offers an introduction to market design, providing students with a broad overview of issues related to the design and analysis of market mechanisms. It defines a market as a demand and a supply, without specifying a price system or mechanism. This allows the text to analyze a broad set of situations—including such unconventional markets as college admissions and organ donation—and forces readers to pay attention to details that might otherwise be overlooked. Students often complain that microeconomics is too abstract and disconnected from reality; the study of market design shows how theory can help solve existing, real-life problems. The book focuses on the interplay between theory and applications. To keep the text as accessible as possible, special effort has been made to minimize formal description of the models while emphasizing the intuitive, with detailed explanations and resolution of examples. Appendixes offer general reviews of elements of game theory and mechanism design that are related to the themes explored in the book, presenting the basic concepts with as many explanations and illustrations as possible. The book covers topics including the basics of simple auctions; eBay auctions; Vickrey–Clarke–Groves auctions; keyword auctions, with examples from Google and Facebook; spectrum auctions; financial markets, with discussions of treasury auctions and IPOs; trading on the stock market; the basic matching model; medical match; assignment problems; probabilistic assignments; school choice; course allocation, with examples from Harvard and Wharton; and kidney exchange.