*5.1. Model*

We use our model of binary actions with prior beliefs introduced in Section 4.1, with actions *A* = {buy, sell}. The decision functions are then given by

$$\begin{aligned} f\_t[\text{buy}|\mathbf{x}] &= \frac{1}{Z\_{t,\mathbf{x}}} p\_t[\text{buy}|e^{\frac{\|I[\mathbf{x},\mathbf{b}\mathbf{u}\mathbf{y}]}{I}} \\ f\_t[\text{sell}|\mathbf{x}] &= \frac{1}{Z\_{t,\mathbf{x}}} p\_t[\text{sell}|e^{\frac{\|I[\mathbf{x},\mathbf{s}\mathbf{u}\mathbf{l}]}{I}} \\ Z\_{t,\mathbf{x}} &= f\_t[\text{buy}|\mathbf{x}] + f\_t[\text{sell}|\mathbf{x}] \end{aligned} \tag{24}$$

where we explore a range of *pt* (prior at time *t*) functions, discussing their effects on decision-making and resulting probability distributions.
