A model for the stopping behavior of users of online systems

We examine a model in which the user of an online system continually updates his/her estimated probability of success, and quits or continues according to the expected utility of each action. The prior distribution of the unknown probability is a beta distribution, with mean determined by the a priori expectation of success, and variance determined by the confidence with which the user has that prior expectation. The stopping criterion depends upon the accumulated number of positive and negative reinforcements, and is a straight line in a suitable coordinate system.