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001 9781947287215
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006 m eo d
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008 190719r20192019nyua ob 001 0 eng d
020 _a9781947287215
_qeBook
020 _a9781947287222
_qePub
020 _z9781947287239
_qhardcover
020 _z9781947287208
_qpaperback
024 8 _a10.1145/3241304
_2doi
035 _a(CaBNVSL)thg00979248
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA269
_b.R835 2019eb
082 0 4 _a519.3
_223
100 1 _aRubinstein, Aviad,
_eauthor.
245 1 0 _aHardness of approximation between P and NP /
_cAviad Rubinstein.
250 _aFirst edition.
264 1 _a[New York, New York] :
_bAssociation for Computing Machinery,
_c[2019]
300 _a1 PDF (xv, 301 pages) :
_billustrations (chiefly color).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _aACM books,
_x2374-6777 ;
_v#24
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader.
500 _aRevision of author's thesis (doctoral)--University of California, Berkeley, 2017.
504 _aIncludes bibliographical references (pages [273]-290) and index.
505 0 _apart I. Overview -- 1. The frontier of intractability -- 1.1. PPAD : finding a needle you know is in the haystack -- 1.2. Quasi-polynomial time and the birthday paradox -- 1.3. Approximate Nash equilibrium
505 8 _a2. Preliminaries -- 2.1. Nash equilibrium and relaxations -- 2.2. PPAD and end-of-a-line -- 2.3. Exponential time hypotheses -- 2.4. PCP theorems -- 2.5. Learning theory -- 2.6. Information theory -- 2.7. Useful lemmata
505 8 _apart II. Communication complexity -- 3. Communication complexity of approximate Nash equilibrium -- 3.1. Uncoupled dynamics -- 3.2. Techniques -- 3.3. Additional related literature -- 3.4. Proof overview -- 3.5. Proofs -- 3.6. An open problem : correlated equilibria in 2-player games
505 8 _a4. Brouwer's fixed point -- 4.1. Brouwer with �[infinity] -- 4.2. Euclidean Brouwer
505 8 _apart III. PPAD -- 5. PPAD-hardness of approximation
505 8 _a6. The generalized circuit problem -- 6.1. Proof overview -- 6.2. From Brouwer to [epsilon]-Gcircuit -- 6.3. Gcircuit with fan-out 2
505 8 _a7. Many-player games -- 7.1. Graphical, polymatrix games -- 7.2. Succinct games
505 8 _a8. Bayesian Nash equilibrium -- 9. Market equilibrium -- 9.1. Why are non-monotone markets hard? -- 9.2. High-level structure of the proof -- 9.3. Adaptations for constant factor inapproximability -- 9.4. Non-monotone markets : proof of inapproximability
505 8 _a10. CourseMatch -- 10.1. The course allocation problem -- 10.2. A-CEEI is PPAD-hard -- 10.3. A-CEEI [epsilon] PPAD
505 8 _apart IV. Quasi-polynomial time -- 11. Birthday repetition -- 11.1. Warm-up : best [epsilon]-Nash
505 8 _a12. Densest k-subgraph -- 12.1. Construction (and completeness) -- 12.2. Soundness
505 8 _a13. Community detection -- 13.1. Related works -- 13.2. Overview of proofs -- 13.3. Hardness of counting communities -- 13.4. Hardness of detecting communities
505 8 _a14. VC and Littlestone's dimensions -- 14.1. Discussion -- 14.2. Techniques -- 14.3. Related Work -- 14.4. Inapproximability of the VC dimension -- 14.5. Inapproximability of Littlestone's dimension -- 14.6. Quasi-polynomial algorithm for Littlestone's dimension
505 8 _a15. Signaling -- 15.1. Techniques -- 15.2. Near-optimal signaling is hard
505 8 _apart V. Approximate Nash equilibrium -- 16. 2-player approximate Nash equilibrium -- 16.1. Technical overview -- 16.2. End-of-a-line with local computation -- 16.3. Holographic proof -- 16.4. Polymatrix WeakNash -- 16.5. From Polymatrix to Bimatrix.
520 3 _aNash 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.
530 _aAlso available in print.
588 _aTitle from PDF title page (viewed on July 19, 2019).
650 0 _aGame theory.
650 0 _aProgramming (Mathematics)
776 0 8 _iPrint version:
_z9781947287239
_z9781947287208
856 4 2 _3Abstract with links to full text
_uhttps://dl.acm.org/citation.cfm?id=3241304
999 _c891
_d891