On the Linear Model with Two Absorbing Barriers

A family of linear models for learning in two-choice situations is considered. These models have in common the assumption that nonreward has no effect on response probability. The function r(p) that relates asymptotic probability of one of the responses to its initial probability is studied intensively. It is shown to be closely related to the total number x(p) of response alternations. The asymptotic probability of making the less favorable response is shown to be small when the learning rates associated with reward are small, Finally, some of the basic analytic function theoretic properties of r(p) are presented.