Prediction and Interaction

EES 4760/5760

Agent-Based & Individual-Based Computational Modeling

Jonathan Gilligan

Class #13: Tuesday, Feb. 20 2018

Getting Started

Getting Started

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Prediction

Prediction

  • What do investors want?
    • Maximize their wealth over time
  • How do investors decide what patch to move to?
    • Predict what their wealth is likely to be after a certain number of ticks on each square. \[ U = (W + P \times T) \times (1 - F)^T \]
  • Farmer planting crops
    • Predict what weather will be
    • Predict what crops will be in demand at end of season
    • Past experience, statistical analysis, …
  • Predator chasing prey
    • Predict where prey will be in order to intercept
    • Extrapolate from current position, velocity …

Modeling Prediction

  • Sensing: What do agents know?
  • Cognition: How do agents think?
  • Learning: Do agents learn from experience?

Business Investor

  • How does agent decide how far into the future to try to predict expected utility?
  • How does this time horizon affect behaviors and outcomes?

Varying Time Horizon: Wealth

Varying Time Horizon: Failures

Varying Time Horizon: Profit

Varying Time Horizon: Risk

Modeling Prediction

Investor Ignorance

  • Suppose the investor does not know risks of failure?
  • Learn about risk from experience
  • Bayesian updating:
    • Start assuming that each patch has same risk (average)
    • Each turn investors get new information about failures
    • beta function: \[F_{\text{est}} = \frac{\alpha}{\alpha + \beta}\] What are \(\alpha\) and \(\beta\)?
    • \(\alpha\) represents number of failures on a patch
    • \(\beta\) represents number of non-failures
    • Initial guess: \[\begin{aligned} \alpha &= (R^2 - R^3 - RV) / V\\ \beta &= (R/V) (1 - R^2) + (R - 1), \end{aligned}\] where \(R\) is the average risk across patches and \(V\) is the variance of risk across patches.
    • Every tick, increment \(\alpha\) for patches with failures and increment \(\beta\) for patches without failures.

Experiment

  • Open BusinessInvestor_bayesian.nlogo