A Continuous-time Tractable Model for Present-biased Agents

TL;DR

This paper introduces a new continuous-time mathematical model for present-biased agents, enabling better prediction and intervention strategies for behaviors influenced by immediate reward overvaluation.

Contribution

The study develops a novel continuous-time model that is analytically tractable and accommodates various discount functions, advancing understanding of present bias in behavioral economics.

Findings

Derived optimal intervention strategies for exponential and hyperbolic discounting.

Model retains analytical tractability while handling diverse discount functions.

Provides theoretical insights into managing present-biased behavior.

Abstract

Present bias, the tendency to overvalue immediate rewards while undervaluing future ones, is a well-known barrier to achieving long-term goals. As artificial intelligence and behavioral economics increasingly focus on this phenomenon, the need for robust mathematical models to predict behavior and guide effective interventions has become crucial. However, existing models are constrained by their reliance on the discreteness of time and limited discount functions. This study introduces a novel continuous-time mathematical model for agents influenced by present bias. Using the variational principle, we model human behavior, where individuals repeatedly act according to a sequence of states that minimize their perceived cost. Our model not only retains analytical tractability but also accommodates various discount functions. Using this model, we consider intervention optimization problems under exponential and hyperbolic discounting and theoretically derive optimal intervention strategies, offering new insights into managing present-biased behavior.