Hardness Approximation by Aviad Rubinstein (44 results)
- Softcover
Seller: Brook Bookstore On Demand, Napoli, NA, ItalyBrook Bookstore On Demand
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- Softcover
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- Hardcover
Seller: Brook Bookstore On Demand, Napoli, NA, ItalyBrook Bookstore On Demand
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- Softcover
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Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
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Language: English
Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
Seller: PBShop.store UK, Fairford, GLOS, United KingdomPBShop.store UK
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- Softcover
Seller: Majestic Books, Hounslow, United KingdomMajestic Books
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- Softcover
Seller: GreatBookPricesUK, Woodford Green, United KingdomGreatBookPricesUK
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- Hardcover
- First Edition
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, IrelandKennys Bookshop and Art Galleries Ltd.
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Language: English
Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
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- Softcover
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- Softcover
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Condition: New. pp. 320.
Language: English
Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
Seller: GreatBookPrices, Columbia, MD, U.S.A.GreatBookPrices
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- Softcover
Seller: Ria Christie Collections, Uxbridge, United KingdomRia Christie Collections
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- Softcover
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- Softcover
Seller: GreatBookPricesUK, Woodford Green, United KingdomGreatBookPricesUK
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Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
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Language: English
Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
Seller: Majestic Books, Hounslow, United KingdomMajestic Books
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- Softcover
Seller: Leopolis, Kraków, PolandLeopolis
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£ 57.26
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Soft cover. Condition: New. 8vo (23.5 cm), XV, 304 pp. Laminated wrappers. "Since Nash's original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade… ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed. Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer's fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games." (from the publisher's synopsis).
Language: English
Published by Morgan and Claypool Publishers, US, 2019
Series: Book 12 of 17 - ACM Books
- Softcover
Seller: Rarewaves.com USA, London, LONDO, United KingdomRarewaves.com USA
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£ 116.38
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Paperback. Condition: New. Nash equilibrium is the central solution concept in Game Theory.Since Nash's original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and… more. A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed.Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games.The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer's fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games.
- Hardcover
Seller: Kennys Bookstore, Olney, MD, U.S.A.Kennys Bookstore
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£ 111.23
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Condition: New. 2019. 1st Edition. hardcover. . . . . . Books ship from the US and Ireland.
- Softcover
Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
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Paperback. Condition: Brand New. 319 pages. 9.25x7.50x0.94 inches. In Stock.
Language: English
Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
Seller: Ria Christie Collections, Uxbridge, United KingdomRia Christie Collections
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£ 106.11
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Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
Seller: Books Puddle, New York, NY, U.S.A.Books Puddle
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Language: English
Published by Association for Computing Machinery, 2019
Series: Book 12 of 17 - ACM Books
- Hardcover
Seller: GreatBookPricesUK, Woodford Green, United KingdomGreatBookPricesUK
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£ 105.84
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- Hardcover
Seller: THE SAINT BOOKSTORE, Southport, United KingdomTHE SAINT BOOKSTORE
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£ 104.45
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- Hardcover
Seller: Leopolis, Kraków, PolandLeopolis
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£ 71.58
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Hardcover. Condition: New. 8vo (24.5 cm), XV, 304 pp. Publisher's laminated boards. "Since Nash's original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more.… A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed. Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer's fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games." (from the publisher's synopsis).
