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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?

# 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