Preface xi1 Introduction 11.1 A Number of Economic Applications 11.2 A Mix of Techniques 31.3 Brief History 41.4 Literature 51.5 About These Notes 61.6 Organization of This Book 71.7 Notation and Conventions 92 Monge-Kantorovich Theory 112.1 Couplings 112.2 Optimal Couplings 132.3 Monge-Kantorovich Duality 142.4 Equilibrium 182.5 A Preview of Applications 192.6 Exercises 222.7 References and Notes 233 The Discrete Optimal Assignment Problem 243.1 Duality 253.2 Stability 263.3 Pure Assignments 273.4 Computation via Linear Programming 293.5 Exercises 323.6 References and Notes 334 One-Dimensional Case 344.1 Copulas and Comonotonicity 354.2 Supermodular Surplus 364.3 The Wage Equation 404.4 Numerical Computation 424.5 Exercises 434.6 References and Notes 445 Power Diagrams 455.1 Hotelling's Location Model 455.2 Capacity Constraints 485.3 Computation via Convex Optimization 535.4 Exercises 545.5 References and Notes 566 Quadratic Surplus 576.1 Convex Analysis from the Point of View of Optimal Transport 576.2 Main Results 606.3 Vector Quantiles 636.4 Polar Factorization 656.5 Computation by Discretization 686.6 Exercises 696.7 References and Notes 707 More General Surplus 727.1 Generalized Convexity 727.2 The Main Results 767.3 Computation by Entropic Regularization 787.4 Exercises 797.5 References and Notes 808 Transportation on Networks 818.1 Setup 828.2 Optimal Flow Problem 878.3 Integrality 908.4 Computation via Linear Programming 918.5 Exercises 938.6 References and Notes 949 Some Applications 959.1 Random Sets and Partial Identification 959.2 Identification of Discrete Choice Models 989.3 Hedonic Equilibrium 1019.4 Identification via Vector Quantile Methods 1049.5 Vector Quantile Regression 1069.6 Implementable Mechanisms 1109.7 No-Arbitrage Pricing of Financial Derivatives 1159.8 References and Notes 11710 Conclusion 11810.1 Mathematics 11810.2 Computation 11910.3 Duality 12010.4 Toward a Theory of "Equilibrium Transport" 12210.5 References and Notes 123A Solutions to the Exercises 125A.1 Solutions for Chapter 2 125A.2 Solutions for Chapter 3 128A.3 Solutions for Chapter 4 130A.4 Solutions for Chapter 5 133A.5 Solutions for Chapter 6 137A.6 Solutions for Chapter 7 139A.7 Solutions for Chapter 8 141B Linear Programming 144B.1 Minimax Theorem 144B.2 Duality 144B.3 Link with Zero-Sum Games 146B.4 References and Notes 148C Quantiles and Copulas 149C.1 Quantiles 149C.2 Copulas 151C.3 References and Notes 153D Basics of Convex Analysis 154D.1 Convex Sets 154D.2 Convex Functions 155D.3 References and Notes 159E McFadden's Generalized Extreme Value Theory 160E.1 References and Notes 160References 161Index 169