2024/09/17 by Yasunori Akagi, Akagi, Yasunori, Hideaki Kim +3 · 1 citation
Computer Science · #Cellular Automata and Applications #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2409.11225
openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.