By force of habit: Self-trapping in a dynamical utility landscape

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximization. We propose a stylized model with a history-dependent utility function, where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find, in particular, that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behavior.