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Table of contents
List of Figures
1 outline
2 introduction
2.1 Overview
2.2 The Microfoundations conundrum
2.3 Agent-based models – the way ahead
2.4 Applications of ABMs
2.5 Statistical Physics and ABMs
2.6 Contributions of this Thesis
3 background
3.1 Constraint Satisfaction Problems
3.2 From CSPs to Statistical mechanics
3.3 Back to K-SAT
3.4 Continuous CSPs — The Perceptron
3.5 The Perceptron as a learning problem
3.6 Perceptron and sphere packing
3.7 Discussion
4 self-planting in the perceptron csp
4.1 A few preliminaries
4.2 Phase diagram of the Perceptron CSP
4.3 Planting and Self-planting
4.4 “Remove and Replace” Dynamics
4.4.1 Long-time behavior of the energy
4.4.2 The R&R Transition
4.4.3 Interpreting the algorithmic transition
4.4.4 Energy landscape dynamics
4.5 Discussion & Conclusion
5 a csp based agent-based model
5.1 Overview
5.2 The Economy as a constraint satisfaction problem
5.2.1 Budget constraint and formation of prices
5.2.2 Preferences update: supply and demand
5.2.3 Transactions, production costs and redistribution .
5.2.4 Removal and Replacement of agents
5.2.5 Summary of the parameters
5.3 Reducing the space of parameters
5.4 Role of the debt limit: Macro-level
5.5 Role of the debt limit: Dynamics
5.6 Discussion & Conclusion
6 simulating covid-like shocks to an abm
6.1 Description of Mark-0
6.1.1 Households
6.1.2 Firms
6.1.3 Banking sector
6.2 Summary
6.3 Simulating shocks to the economy
6.4 Policy proposals for a quick recovery
6.5 Discussion & Conclusion
7 summary and conclusions
7.1 Summary of the major results
7.2 Perspectives
7.3 Broader purpose
a derivation of the perceptron phase diagram
a.1 Setting up the problem
a.2 Calculation of the partition function
a.3 Hierarchical ansatz for qab
a.3.1 Some preliminary details
a.4 Reformulation in terms of the magnetization m
a.5 Replica Symmetric Solution
a.5.1 SAT Phase
a.5.2 UNSAT Phase
a.5.3 Jamming Limit
a.5.4 Stability Analysis
a.5.5 Phase diagram
references
