Time Inconsistency, Self-Control and Internal Harmony: A Planner-Doer Game Framework

Abstract

For time inconsistent multi-period mean-variance portfolio decision, we develop a two-tier planner-doer game model with self-control, in which planner and doers represent different interests of the same investor at different time instants and planner (the willpower to resist short term temptations) can impact preferences of doers through commitment by punishment, while the applied total penalty in turn affects the planner’s preference. Dealing with time inconsistency is to achieve a degree of internal harmony (measured quantitatively by expected cost of self-control) through aligning interests of planner and doers. We further extend this game framework to general time inconsistent stochastic decision problems.