Economic Networks: Theory and Computation by Thomas 9781009456333 1009456334

Economic Networks: Theory and Computation Thomas J. Sargent – Ebook Instant Download/Delivery ISBN(s): 9781009456333, 1009456334

Product details:

• ISBN 10:1009456334
• ISBN 13:9781009456333
• Author: Thomas 

Economic Networks
Theory and Computation

Table contents:

Common Symbols
1 Introduction
1.1 Motivation
1.2 Spectral Theory
1.2.1 Eigendecompositions
1.2.2 The Neumann Series Lemma
1.2.3 The Perron–Frobenius Theorem
1.3 Probability
1.3.1 Discrete Probability
1.3.2 Power Laws
1.4 Graph Theory
1.4.1 Unweighted Directed Graphs
1.4.2 Weighted Digraphs
1.4.3 Network Centrality
1.4.4 Scale-Free Networks
1.5 Chapter Notes
2 Production
2.1 Multisector Models
2.1.1 Production Networks
2.1.2 Equilibrium
2.1.3 Demand Shocks
2.1.4 Forward Linkages
2.2 General Equilibrium
2.2.1 Supply and Demand
2.2.2 The Granular Hypothesis
2.2.3 Network Structure and Shock Propagation
2.3 More Spectral Theory
2.3.1 Vector Norms
2.3.2 Matrix Norms
2.3.3 Iteration in Matrix Space
2.3.4 Exact Stability Conditions
2.4 Chapter Notes
3 Optimal Flows
3.1 Shortest Paths
3.1.1 Definition and Examples
3.1.2 Bellman’s Method
3.1.3 Betweenness Centrality
3.2 Linear Programming and Duality
3.2.1 Linear Assignment
3.2.2 Linear Programming
3.3 Optimal Transport
3.3.1 The Monge–Kantorovich Problem
3.3.2 Kantorovich Duality
3.3.3 Optimal Transport and Competitive Equilibria
3.3.4 The General Flow Problem
3.4 Chapter Notes
4 Markov Chains and Networks
4.1 Markov Chains as Digraphs
4.1.1 Markov Models
4.1.2 Distribution Dynamics
4.1.3 Stationarity
4.2 Asymptotics
4.2.1 Ergodicity
4.2.2 Aperiodicity and Stability
4.2.3 The Markov–Dobrushin Coefficient
4.2.4 Information and Social Networks
4.3 Chapter Notes
5 Nonlinear Interactions
5.1 Fixed Point Theory
5.1.1 Contraction Mappings
5.1.2 Shortest Paths Revisited
5.1.3 Supply Constraints
5.1.4 Fixed Points and Monotonicity
5.2 Financial Networks
5.2.1 Contagion
5.2.2 Default Cascades
5.2.3 Equity Cross-Holdings
5.3 Chapter Notes
Appendix A Math Review
A.1 Sets and Functions
A.1.1 Sets
A.1.2 Equivalence Classes
A.1.3 Functions
A.1.4 Inverse Functions
A.1.5 Real-Valued Functions
A.1.6 Fixed Points
A.1.7 Vectors
A.1.8 Complex Numbers
A.2 Order
A.2.1 Partial Orders
A.2.2 Pointwise Operations on Vectors
A.2.3 Monotonicity
A.3 Convergence
A.3.1 Metric Properties of the Real Line
A.3.2 Metric Properties of Euclidean Space
A.3.3 Topology
A.3.4 Continuity in Vector Space
A.4 Linear Algebra
A.4.1 Subspaces and Independence
A.4.2 Basis Vectors and Dimension
A.4.3 Linear Maps Are Matrices
A.4.4 Linear Hyperplanes
A.4.5 Nonsingular Linear Systems
A.4.6 Orthogonality
A.5 Convexity and Concavity
A.5.1 Convexity and Polyhedra
A.5.2 Convex and Concave Functions
A.6 Optimization
A.6.1 Definitions and Existence
A.6.2 Convexity and Extrema
A.6.3 Multivariate Quadratic Objectives
A.7 Lagrangian Duality
A.7.1 Theory
A.7.2 Saddle Points and Duality
A.7.3 Karush, Kuhn, and Tucker

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