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- 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 …

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

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

- Interactive app https://alo.ees.vanderbilt.edu/shiny/ees4760/contour/

- 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.

- Open
`BusinessInvestor_bayesian.nlogo`