Part IV: Agent-Based Models
Individual-level models of urban agents — residential segregation dynamics, land market equilibrium, and pedestrian movement. Emergent collective patterns from simple micro-level decision rules.
Part Overview
Individual-level models of urban agents — residential segregation dynamics, land market equilibrium, and pedestrian movement. Schelling's threshold model produces macro-segregation from mild micro-preferences, the Alonso-Muth-Mills bid-rent curve yields an exponential rent gradient \(p(r) \propto e^{-tr/q^*}\), and Helbing's Social Force model governs pedestrian flow through urban spaces.
Key Topics
- • Schelling segregation model
- • Entropy-based segregation index
- • Alonso-Muth-Mills bid-rent
- • Exponential rent gradient \(p(r) \propto e^{-tr/q^*}\)
- • Logit discrete choice
- • Helbing Social Force model
3 chapters | Micro decisions, macro patterns | Agents shaping urban form
Chapters
Chapter 1: Schelling Segregation
Schelling's checkerboard model demonstrates how mild individual preferences for same-type neighbors produce extreme macro-level segregation. Entropy-based segregation indices quantify the emergent pattern.
Chapter 2: Bid-Rent Gradient
The Alonso-Muth-Mills monocentric city model. Households maximize utility subject to commuting cost, producing an exponential rent gradient \(p(r) \propto e^{-tr/q^*}\) and logit discrete choice for location selection.
Chapter 3: Social Force Model
Helbing's Social Force model treats pedestrians as particles subject to desired-velocity driving, repulsive interaction forces, and wall boundaries. Lane formation and crowd dynamics emerge naturally.