Hardness of Approximation Between P and NP. Aviad Rubinstein

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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 Chapter 2 Preliminaries Notation 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 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

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