Present bias in partially sophisticated and assisted agents

The well-studied phenomenon of present bias describes how people over-weight costs and rewards incurred in the present. This leads people to put off portions of a task until later, which can cause them to complete tasks in inefficient ways. Using the graphical model of Kleinberg and Oren (2014) to study present bias, previous work has considered agents who are unaware of the effects of their present bias (naive agents) and those who are aware of its effects on the entire task (sophisticated agents). In this paper we use the executive functions of working memory and cognitive flexibility from the psychology literature to introduce a new way of understanding the decision making of these agents which is particularly appropriate for large or complicated tasks. This allows us to define and analyze a new kind of partially sophisticated agent who uses sophisticated reasoning on only part of a task at a time. The main result of this paper shows that in the worst case the performance on a task for each of these different types of agents fits a simple formula which depends only on their present bias and the number of plans the agent needs to make to complete the task. We also define a new commitment device, where an external agent can assist in the completion of a task, and show that the formula still holds with an appropriate modification.