Agent Based Modeling

• An Agent Based Model (ABM) is a computational model that involves simulating the agents, and their actions and interactions within a system with the goal of understanding large scale behaviors and outcomes.

• ABMs are useful for studying complex systems especially those that feature emergent structures or phenomena. It allows for analyzing systemic behaviors from the bottom up.

• ABMs are primarily motivated by difficulties in modeling phenomena via mathematical or or conceptual models.

Theory §

• Incorporate heterogeneity within the system. Rather than having representative agents for large clusters of agents, embrace the heterogeneity.

• Matching the scale of a model to the data can be important

• Move beyond rational agents. Incorporate limited information and bounded rationality. A typology of agents can be found below:

  • Simple agents - the behavior is mostly random but there is a goal. Agents do not maintain internal models and only react to the environment based on immediate self interest
  • Learning Agents - agents maintain a model of the environment.
    • Individual Learning - agents learn data from the environment and update its internal model
    • Social Learning - agents build models of other agents or individual agents.
    • Group Learning - agents learn to behave as a group.
  • Behavioral Agents - agents which are made to reproduce the results of experiments. This also allows us to scale from lab results to simulation results.
  • Other Agents include
    • Cognitive Agents where agents have cognitive abilities
    • Emotive Agents - agents with simulated emotions that can affect their decision processes
    • Deontic Agents -agents that can form their own goals out of obligation or social norms.

• Match the actual processes being simulated.

• Model the agent interactions. Some methods include:

  • Networks
  • Agent interaction regimes — only some agents are active at any given time step.
    • This avoids perfect synchrony which has some advantages
      • It avoids meaningless artifacts in the model output
      • The real world is often asynchronous.
    • Some common regimes:
      • Uniform Activation - agents are activated sequentially. To avoid artifacts, ensure the order is randomized.
      • Random Activation - agents have a random chance of being activated.
      • Poisson clock activation - agents are active based on a schedule determined via a Poisson distribution.
    • It is also possible to have endogenous activation where agents decide when to be active.

• Explore hierarchies within the system.

• Explore emergent superstructures that form as a result of agent interactions.

• Consider incorporating real world data

  • Use agent models to qualitatively reproduce aggregate patterns.
  • Use agent models to quantitatively reproduce aggregate data.
  • Use agent models to quantitatively reproduce micro-data.

• The common pipeline for creating an ABM is:

  • Design the model and the theory behind it.
  • Codify the rules of the model into code.
  • Hyperparameters tuning and validation
  • Model analysis

• ¹ suggests we should also consider data driven ABMs.

  • The recent trend toward data-driven ABMs is helping overcome their traditional limitations of lacking mathematical rigor and feeling arbitrary because of difficulties in calibration.
    • The data driven approach can replace unnecessary assumption
    • They can also help make reasonable assumptions by measuring which assumptions improve results (i.e., how they match real world data).
  • ABMs are data driven when the parameters in the ABM are obtained based on empirical data.
  • Generally there are three methods for making ABMs more data driven
    • Calibration involves modifying the parameters to match empirical data. For parameters where there is no source of empirical or theoretical data, we can infer the data via a machine-learning like process
      • Sampling guesses for these parameters
      • Using summary statistics from simulated and real data
      • Defining a loss function to compare simulated and real data.
      • Choosing parameters to minimize loss.
    • Initialization involves estimating agent-level attributes and initial conditions.
      • Initialization requires to make disparate sources of data compatible with themselves and with the model.
      • Some procedures include
        • Generating synthetic populations
        • Reconstructing a network (if given).
        • Use data, if not from the target source, something analogous to the target source.
    • Assimilation involves estimating the entire time series of agent-specific variables.
      • Use a Kalman filter to combine models and observations.
      • Use PGMs.
      • Use heuristics

Data Driven ABM typology. Image taken from Pangallo and del Rio-Chanona (2024)

Opportunities and Challenges §

• Incorporate micro-data to the model itself.
• Model the full population of the system.
• Optimization - in particular considering hardware and parallelism.
• The Curse of Dimensionality - more parameters in the ABM give rise to exponential search spaces
• Using ABM for forecasting.
• Using ABM as a teaching tool.

Applications §

• Some historic models:

  • The Schelling model for modeling segregation.
  • The Axelrod model of the iterated prisoner’s dilemma
  • Traffic and Pedestrian Flow models.
  • Epidemiology models (i.e the SRI model).
  • Ecological models (i.e., Predator Prey)
  • Political models
    • International relations
    • Voting dynamics
  • Sociological models
    • Demography
    • Dynamics of propagating cultural behavior.
    • Simulating societies
    • Modeling inequality.
  • Urban dynamics

• Computational Economics

Links §

• Game Theory
• Network Science
• Machine Learning

Footnotes §

1. Pangallo and del Rio-Chanona (2024) Data Driven Economic Agent-Based Models ↩