I'm Not Sure What to Think About Them: Non-Bayesian Updating for Naive Present-Biased Players

Abstract

Using a stylized model of group production, we investigate challenges that arise when introducing naive present bias into multi-player games. In particular, we tackle the question of how, when discovering their own present bias, a naive player — who perceives this discovery as a zero-probability event — updates their beliefs regarding their partner's present bias as well as higher-order beliefs regarding both players' present biases. Our analysis demonstrates how equilibrium behavior and outcomes can be highly dependent on the "direction'' with which naive players reassess their prior beliefs. In some situations, a naive player may actually become more inclined to exert effort in pursuit a future reward upon discovering their own present bias. The analysis also shows how naive players can, under the right circumstances, overcome coordination issues that would not be overcome by sophisticated players. More broadly, our approach offers a potential path forward for modeling interactions among naive players.

Keywords: hyperbolic discounting, present bias, teams, motivation, procrastination, higher-order beliefs, non-Bayesian updating, null events

JEL Classification: C72