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Author: Peter Troyan Publisher: ISBN: Category : Languages : en Pages : 43
Book Description
We propose a solution to the trade-off between Pareto efficiency and stability in matching markets. We define a matching to be essentially stable if any claim initiates a chain of reassignments that ultimately results in the initial claimant losing the object she claimed to a third agent. Our definition is not only compatible with Pareto efficiency but also is practical, since explaining why claims are not valid is straightforward. We study the essentially stable set and show that it shares some, though not all, of the structure possessed by the stable set. We classify popular Pareto efficient mechanisms using our definition: those based on Shapley and Scarf's TTC mechanism are not essentially stable while Kesten's EADA mechanism is. Our analysis points to a trade-off among essential stability, Pareto efficiency, and strategy proofness: mechanisms exist that satisfy any two of these properties but no mechanism achieves all three.
Author: Peter Troyan Publisher: ISBN: Category : Languages : en Pages : 43
Book Description
We propose a solution to the trade-off between Pareto efficiency and stability in matching markets. We define a matching to be essentially stable if any claim initiates a chain of reassignments that ultimately results in the initial claimant losing the object she claimed to a third agent. Our definition is not only compatible with Pareto efficiency but also is practical, since explaining why claims are not valid is straightforward. We study the essentially stable set and show that it shares some, though not all, of the structure possessed by the stable set. We classify popular Pareto efficient mechanisms using our definition: those based on Shapley and Scarf's TTC mechanism are not essentially stable while Kesten's EADA mechanism is. Our analysis points to a trade-off among essential stability, Pareto efficiency, and strategy proofness: mechanisms exist that satisfy any two of these properties but no mechanism achieves all three.
Author: Dan Gusfield Publisher: ISBN: 9780262515528 Category : Combinatorial analysis Languages : en Pages : 0
Book Description
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.
Author: Dan Gusfield Publisher: MIT Press (MA) ISBN: 9780262071185 Category : Computers Languages : en Pages : 240
Book Description
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.
Author: Alvin E. Roth Publisher: Cambridge University Press ISBN: 1107782430 Category : Business & Economics Languages : en Pages : 288
Book Description
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
Author: Tomás Feder Publisher: American Mathematical Soc. ISBN: 0821803476 Category : Computers Languages : en Pages : 242
Book Description
The structural and algorithmic study of stability in nonexpansive networks is based on a representation of the possible assignments of Boolean values for a network as vertices in a Boolean hypercube under the associated Hamming metric. This global view takes advantage of the median properties of the hypercube, and extends to metric networks, where individual values are now chosen from the finite metric spaces and combined by means of an additive product operation. The relationship between products of metric spaces and products of graphs then establishes a connection between isometric representation in graphs and nonexpansiveness in metric networks.
Author: Marios Mavronicolas Publisher: Springer ISBN: 3642046452 Category : Computers Languages : en Pages : 369
Book Description
This book constitutes the refereed proceedings of the Second International Symposium on Algorithmic Game Theory, SAGT 2009, held in Paphos, Cyprus, in October 2009. The 29 revised full papes presented together with 3 invited lectures were carefully reviewed and selected from 55 submissions. The papers are intended to cover all important areas such as solution concepts, game classes, computation of equilibria and market equilibria, algorithmic mechanism design, automated mechanism design, convergence and learning in games, complexity classes in game theory, algorithmic aspects of fixed-point theorems, mechanisms, incentives and coalitions, cost-sharing algorithms, computational problems in economics, finance, decision theory and pricing, computational social choice, auction algorithms, price of anarchy and its relatives, representations of games and their complexity, economic aspects of distributed computing and the internet, congestion, routing and network design and formation games and game-theoretic approaches to networking problems.
Author: David F. Manlove Publisher: World Scientific ISBN: 9814425257 Category : Mathematics Languages : en Pages : 524
Book Description
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."
Author: Michael Jay Szestopalow Publisher: ISBN: Category : Languages : en Pages : 74
Book Description
Stable matchings were introduced in 1962 by David Gale and Lloyd Shapley to study the college admissions problem. The seminal work of Gale and Shapley has motivated hundreds of research papers and found applications in many areas of mathematics, computer science, economics, and even medicine. This thesis studies stable matchings in graphs and hypergraphs. We begin by introducing the work of Gale and Shapley. Their main contribution was the proof that every bipartite graph has a stable matching. Our discussion revolves around the Gale-Shapley algorithm and highlights some of the interesting properties of stable matchings in bipartite graphs. We then progress to non-bipartite graphs. Contrary to bipartite graphs, we may not be able to find a stable matching in a non-bipartite graph. Some of the work of Irving will be surveyed, including his extension of the Gale-Shapley algorithm. Irving's algorithm shows that many of the properties of bipartite stable matchings remain when the general case is examined. In 1991, Tan showed how to extend the fundamental theorem of Gale and Shapley to non-bipartite graphs. He proved that every graph contains a set of edges that is very similar to a stable matching. In the process, he found a characterization of graphs with stable matchings based on a modification of Irving's algorithm. Aharoni and Fleiner gave a non-constructive proof of Tan's Theorem in 2003. Their proof relies on a powerful topological result, due to Scarf in 1965. In fact, their result extends beyond graphs and shows that every hypergraph has a fractional stable matching. We show how their work provides new and simpler proofs to several of Tan's results. We then consider fractional stable matchings from a linear programming perspective. Vande Vate obtained the first formulation for complete bipartite graphs in 1989. Further, he showed that the extreme points of the solution set exactly correspond to stable matchings. Roth, Rothblum, and Vande Vate extended Vande Vate's work to arbitrary bipartite graphs. Abeledo and Rothblum further noticed that this new formulation can model fractional stable matchings in non-bipartite graphs in 1994. Remarkably, these formulations yield analogous results to those obtained from Gale-Shapley's and Irving's algorithms. Without the presence of an algorithm, the properties are obtained through clever applications of duality and complementary slackness.
Author: Peter Troyan
Author: Peter Troyan
Author: Dan Gusfield
Author: Dan Gusfield
Author: Alvin E. Roth
Author: Tomás Feder
Author: Hernan Abeledo
Author: Marios Mavronicolas
Author: David F. Manlove
Author: Michael Jay Szestopalow
Author: Simon R. Blackburn