How far to commit to open-loop action: a probabilistic decision approach with analogies to signal-detection theory

A theory for optimizing the extent of a continuous action variable in a situation where either or both a discrete reward and discrete cost occur as probabilistic functions of the extent of the action selected is presented. It is shown how in many respects the approach is similar to signal detection theory, and also that there are the essential differences, especially since the decision is continuous rather than binary. Examples for application are suggested