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From time-inconsistency to time-consistency for optimal stopping problems.

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We quantify time-inconsistency in decision-making by measuring how long it takes naive agents to adopt sophisticated strategies. Higher probability distortion in cumulative prospect theory correlates with greater time-inconsistency and longer adaptation times.

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Area of Science:

  • Decision Theory
  • Behavioral Economics
  • Mathematical Psychology

Background:

  • Time-inconsistent preferences pose challenges in optimal stopping problems.
  • Naive agents often deviate from initial plans due to evolving preferences.
  • Cumulative prospect theory (CPT) accounts for probability distortion, a source of time-inconsistency.

Purpose of the Study:

  • To develop a metric for quantifying the level of time-inconsistency.
  • To investigate the relationship between probability distortion in CPT and the severity of time-inconsistency.
  • To determine the time required for naive strategies to converge to sophisticated ones.

Main Methods:

  • Modeling optimal stopping problems with time-inconsistent preferences.
  • Introducing a repeated experimental framework where agents observe and adjust their behavior.
  • Analyzing the convergence time of naive strategies to sophisticated strategies based on observed actions.

Main Results:

  • The time required to transition from naive to sophisticated strategies serves as a measure of time-inconsistency.
  • For CPT preferences, increased probability distortion leads to greater time-inconsistency.
  • Higher degrees of probability distortion necessitate more time for strategy convergence.

Conclusions:

  • The proposed time-based metric effectively quantifies inherent time-inconsistency.
  • Probability distortion in CPT is a direct driver of increased time-inconsistency.
  • Understanding this relationship is crucial for predicting and managing agent behavior in dynamic decision scenarios.