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Hardness of Approximation Between P and NP. Aviad Rubinstein
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PART II
COMMUNICATION COMPLEXITY
Chapter 3
Communication Complexity of Approximate Nash Equilibrium
Our Results
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
Chapter 4
Brouwer’s Fixed Point
4.1 BROUWER with
ℓ∞
4.2 Euclidean BROUWER
PART III
PPAD
Chapter 5
PPAD-Hardness of Approximation
Chapter 6
The Generalized Circuit Problem
Our Results
6.1 Proof Overview
6.2 From Brouwer to
ϵ
-GCIRCUIT
6.3 GCIRCUIT with Fan-out 2
Chapter 7
Many-Player Games
Related Works: Tractable Special Cases
7.1 Graphical, Polymatrix Games
7.2 Succinct Games
Chapter 8
Bayesian Nash Equilibrium
Chapter 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
Chapter 10
CourseMatch
10.1 The Course Allocation Problem
10.2 A-CEEI Is PPAD-Hard
10.3 A-CEEI ∊ PPAD
PART IV
QUASI-POLYNOMIAL TIME
Chapter 11
Birthday Repetition
11.1 Warm-Up: Best
ϵ
-Nash
Chapter 12
Densest k-Subgraph
12.1 Construction (and Completeness)
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