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Author: Christos Tzamos Publisher: ISBN: Category : Languages : en Pages : 64
Book Description
Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a revenue-optimal auction in multi-item settings cannot be found and implemented computationally efficiently, unless ZPP = P^#^p. This is true even for a single additive bidder whose values for the items are independently distributed on two rational numbers with rational probabilities. Our result is very general: we show that it is hard to compute any encoding of an optimal auction of any format (direct or indirect, truthful or non-truthful) that can be implemented in expected polynomial time. In particular, under well-believed complexity-theoretic assumptions, revenue-optimization in very simple multi-item settings can only be tractably approximated. We note that our hardness result applies to randomized mechanisms in a very simple setting, and is not an artifact of introducing combinatorial structure to the problem by allowing correlation among item values, introducing combinatorial valuations, or requiring the mechanism to be deterministic (whose structure is readily combinatorial). Our proof is enabled by a flow interpretation of the solutions of an exponential-size linear program for revenue maximization with an additional supermodularity constraint.
Author: Christos Tzamos Publisher: ISBN: Category : Languages : en Pages : 64
Book Description
Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a revenue-optimal auction in multi-item settings cannot be found and implemented computationally efficiently, unless ZPP = P^#^p. This is true even for a single additive bidder whose values for the items are independently distributed on two rational numbers with rational probabilities. Our result is very general: we show that it is hard to compute any encoding of an optimal auction of any format (direct or indirect, truthful or non-truthful) that can be implemented in expected polynomial time. In particular, under well-believed complexity-theoretic assumptions, revenue-optimization in very simple multi-item settings can only be tractably approximated. We note that our hardness result applies to randomized mechanisms in a very simple setting, and is not an artifact of introducing combinatorial structure to the problem by allowing correlation among item values, introducing combinatorial valuations, or requiring the mechanism to be deterministic (whose structure is readily combinatorial). Our proof is enabled by a flow interpretation of the solutions of an exponential-size linear program for revenue maximization with an additional supermodularity constraint.
Author: Tim Roughgarden Publisher: Cambridge University Press ISBN: 1316781178 Category : Computers Languages : en Pages : 356
Book Description
Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.
Author: Dirk Bergemann Publisher: World Scientific ISBN: 981437458X Category : Business & Economics Languages : en Pages : 471
Book Description
Foreword by Eric Maskin (Nobel Laureate in Economics, 2007)This volume brings together the collected contributions on the theme of robust mechanism design and robust implementation that Dirk Bergemann and Stephen Morris have been working on for the past decade. The collection is preceded by a comprehensive introductory essay, specifically written for this volume with the aim of providing the readers with an overview of the research agenda pursued in the collected papers.The introduction selectively presents the main results of the papers, and attempts to illustrate many of them in terms of a common and canonical example, namely a single unit auction with interdependent values. It is our hope that the use of this example facilitates the presentation of the results and that it brings the main insights within the context of an important economic mechanism, namely the generalized second price auction.
Author: Georgios Pierrakos Publisher: ISBN: Category : Languages : en Pages : 186
Book Description
This dissertation provides a complexity-theoretic critique of Myerson's theorem, one of Mechanism Design's crown jewels, for which Myerson was awarded the 2007 Nobel Memorial Prize in Economic Sciences. This theorem gives a remarkably crisp solution to the problem faced by a monopolist wishing to sell a single item to a number of interested, rational bidders, whose valuations for the item are distributed independently according to some given distributions; the monopolist's goal is to design an auction that will maximize her expected revenue, while at the same time incentivizing the bidders to bid their true value for the item. Myerson solves this problem of designing the revenue-maximizing auction, through an elegant transformation of the valuation space, and a reduction to the problem of designing the social welfare-maximizing auction (i.e. allocating the item to the bidder who values it the most). This latter problem is well understood, and it admits a deterministic (i.e. the auctioneer does not have to flip any coins) and simple solution: the Vickrey (or second-price) auction. In the present dissertation we explore the trade-offs between the plausibility of this result and its tractability: First, we consider what happens as we shift away from the simple setting of Myerson to more complex settings, and, in particular, to the case of bidders with arbitrarily correlated valuations. Is a characterization as crisp and elegant as Myerson's still possible? In Chapter 2 we provide a negative answer: we show that, for three or more bidders, the problem of computing a deterministic, ex-post incentive compatible and individually rational auction that maximizes revenue is NP-complete --in fact, inapproximable. Even for the case of two bidders, where, as we show, the revenue-maximizing auction is easy to compute, it admits nonetheless no obvious natural interpretation a-la Myerson. Then, motivated by the subtle interplay between social welfare- and revenue-maximizing auctions implied by Myerson's theorem, we study the trade-off between those two objectives for various types of auctions. We show that, as one moves from the least plausible auction format to the most plausible one, the problem of reconciling revenue and welfare becomes less and less tractable. Indeed, if one is willing to settle for randomized solutions, then auctions that fare well with respect to both objectives simultaneously are possible, as shown by Myerson and Satterthwaite. For deterministic auctions on the other hand, we show in Chapter 3 that it is NP-hard to exactly compute the optimal trade-off (Pareto) curve between those two objectives. On the positive side, we show how this curve can be approximated within arbitrary precision for some settings of interest. Finally, when one is only allowed to use variants of the simple Vickrey auction, we show in Chapter 4 that there exist auctions that achieve constant factor approximations of the optimal revenue and social welfare simultaneously.
Author: Rakesh V. Vohra Publisher: Cambridge University Press ISBN: 1139499173 Category : Business & Economics Languages : en Pages : 185
Book Description
Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design.
Author: Paul Milgrom Publisher: Cambridge University Press ISBN: 1139449168 Category : Business & Economics Languages : en Pages : 378
Book Description
This book provides a comprehensive introduction to modern auction theory and its important new applications. It is written by a leading economic theorist whose suggestions guided the creation of the new spectrum auction designs. Aimed at graduate students and professionals in economics, the book gives the most up-to-date treatments of both traditional theories of 'optimal auctions' and newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. The analysis explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. It explores the tension between the traditional theory of auctions with a fixed set of bidders, in which the seller seeks to squeeze as much revenue as possible from the fixed set, and the theory of auctions with endogenous entry, in which bidder profits must be respected to encourage participation.
Author: K. Kudo Publisher: Springer Science & Business Media ISBN: 4431668624 Category : Mathematics Languages : en Pages : 209
Book Description
Nonlinear complex open systems show great diversity in the process of self-organization, and that diversity increases as complexity increases. The measurement of complexity and the origins of the diversity of such complex systems are the focus of interdisciplinary studies extending across a wide range of scientific disciplines that include applied mathematics, physics, chemistry, biology, psychology, ecology, sociology, and economics. Previous investigations have concentrated either on complexity or on diversity, but not both. This volume makes clear the relation between complexity and diversity with examples drawn from various disciplines. Compiles here are presentations from the Complexity and Diversity workshop held in Fugue, Japan, in August 1996. The contributions are the results of research in mathematical systems, physical systems, living systems, and social systems, and are contained in the four corresponding sections of the book. Mathematical expressions for the theory of complexity as a fundamental method along with realistic examples for application of systematic methods provide the reader with ready access to the latest topics in complex systems.
Author: Jean-François Laslier Publisher: Springer Nature ISBN: 3030180506 Category : Business & Economics Languages : en Pages : 507
Book Description
This collection of essays represents responses by over eighty scholars to an unusual request: give your high level assessment of the field of economic design, as broadly construed. Where do we come from? Where do we go from here? The book editors invited short, informal reflections expressing deeply felt but hard to demonstrate opinions, unsupported speculation, and controversial views of a kind one might not normally risk submitting for review. The contributors – both senior researchers who have shaped the field and promising, younger researchers – responded with a diverse collection of provocative pieces, including: retrospective assessments or surveys of the field; opinion papers; reflections on critical points for the development of the discipline; proposals for the immediate future; "science fiction"; and many more. The readers should have fun reading these unusual pieces – as much as the contributors enjoyed writing them.
Author: Petter Ogland Publisher: Lulu.com ISBN: 1387359967 Category : Business & Economics Languages : en Pages : 348
Book Description
'Mechanism Design for Total Quality Management' is clearly written in a logical manner and points are supported by real life case studies. Dr. Ogland demonstrates how a Total Quality Management strategy articulated through the use of bootstrap algorithms can be used to achieve world-class performance in challenging environments such as complex organisations saturated with power struggles and internal politics. The book features insights on critical systems thinking, game theory, quality management systems, the EFQM Business Excellence Model, self-assessment, and the implementation of TQM. Case studies provide practical insights from twenty years of empirical research on how to bootstrap TQM and Business Excellence in complex environments. The ideas developed in the book have been acknowledged as a major contribution to the theory of TQM, and the book itself is an indispensable resource for practitioners trying to implement TQM in environments where traditional implementation methods are bound to fail.
Author: Magnús M. Halldórsson Publisher: Springer ISBN: 3662476665 Category : Computers Languages : en Pages : 751
Book Description
The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed proceedings of the 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised full papers presented were carefully reviewed and selected from 507 submissions. The papers are organized in the following three tracks: algorithms, complexity, and games; logic, semantics, automata and theory of programming; and foundations of networked computation: models, algorithms and information management.
Author: Christos Tzamos
Author: Christos Tzamos
Author: Tim Roughgarden
Author: Dirk Bergemann
Author: Georgios Pierrakos
Author: Rakesh V. Vohra
Author: Paul Milgrom
Author: K. Kudo
Author: Jean-François Laslier
Author: Petter Ogland
Author: Magnús M. Halldórsson