Time-consistent stopping under decreasing impatience

TL;DR

This paper develops a dynamic framework for time-inconsistent stopping problems with decreasing impatience, introducing equilibrium policies via fixed-point iterations and illustrating the approach with a real options example.

Contribution

It provides a novel method to find equilibrium stopping policies in continuous-time models with non-exponential discounting, linking naive and sophisticated behaviors.

Findings

Fixed-point iterations converge to equilibrium policies.

The approach models agent-specific behaviors.

Application to a real options model demonstrates practical relevance.

Abstract

Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in Game Theory, and provides "agent-specific" results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model.