Anxiety-Like Behavioural Inhibition Is Normative under Environmental Threat-Reward Correlations
Fig 2
Finding the approach latency that maximises expected utility.
First time derivatives of expected gain E(G) and negative expected loss −E(L). Under assumptions 7–8 (Model and Methods), the two curves must cross at least once, and that means there must be at least one stationary point. At least one of these stationary points is a maximiser. Crucially, the dotted line shows the impact of a small increase in L or a scaling of p(L). As one can see here, this will shift the optimal approach latency to the right, i. e. to later time points. The argument is formalised using Taylor series (see Model and Methods).