Paper: arXiv 2409.01478

Authors: Pengyu Wei, Wei Wei

Abstract

This paper employs an intra-personal game-theoretic framework to investigate how decreasing impatience influences irreversible investment behaviors in a continuous-time setting. We consider a capacity expansion problem under weighted discount functions, a class of nonexponential functions that exhibit decreasing impatience, including the hyperbolic discount function as a special case. By deriving the Bellman system that characterizes the equilibrium, we establish the framework for analyzing investment behaviors of agents subject to decreasing impatience. From an economic perspective, we demonstrates that decreasing impatience prompts early investment. From a technical standpoint, we warn that decreasing impatience can lead to the failure of the smooth pasting principle.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical exploration of irreversible investment under time-inconsistent weighted discounting, using continuous-time game theory to challenge the validity of the smooth pasting principle. While mathematically dense and conceptually novel from an economic standpoint, it lacks empirical validation, backtesting, or real-world data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Irreversible Investment <br>under Decreasing Impatience] --> B[Inputs: Continuous-Time Capacity Expansion <br>& Weighted Discount Functions]
    B --> C[Methodology: Intra-Personal Game-Theoretic Framework]
    C --> D[Computation: Derive Bellman System <br>for Equilibrium Characterization]
    D --> E[Outcome 1: Decreasing Impatience <br>Prompts Earlier Investment]
    D --> F[Outcome 2: Technical Warning on <br>Failure of Smooth Pasting Principle]

Cited References (39)

  1. Myopia and Inconsistency in Dynamic Utility Maximization (1955)
  2. On second-best national saving and game-equilibrium growth (1968)
  3. Golden eggs and hyperbolic discounting (1997)
  4. Choice and procrastination (2001)
  5. Investment under uncertainty and time-inconsistent preferences (2007)
  6. Subjective discounting in an exchange economy (2003)
  7. Instantaneous gratification (2013)
  8. Investment under uncertainty (1994)
and 31 more
  1. Option exercise games: An application to the equilibrium investment strategies of firms (2002)
  2. Anomalies in intertemporal choice: Evidence and an interpretation (1992)
  3. Super contact and related optimality conditions (1991)
  4. Decreasing impatience: a criterion for Non-stationary time preference and “hyperbolic” discounting (2004)
  5. Weighted discounting—on group diversity, time-inconsistency, and consequences for investment (2020)
  6. Sur les fonctions absolument monotones (1929)
  7. On hyperbolic discounting and uncertain hazard rates (1998)
  8. Proportional discounting of future costs and benefits (1995)
  9. A note on measurement of utility (1937)
  10. Non-constant discounting in continuous time (2007)
  11. Investment and consumption without commitment (2008)
  12. The fragility of time: Time-insensitivity and valuation of the near and far future (2007)
  13. Non-hyperbolic time inconsistency (2009)
  14. Brownian motion and stochastic calculus (2014)
  15. Stochastic controls: Hamiltonian systems and HJB equations (2012)
  16. On time-inconsistent stochastic control in continuous time (2017)
  17. A general theory of Markovian time inconsistent stochastic control problems (2010)
  18. Time-consistent portfolio management (2012)
  19. Optimal investment under uncertainty (1983)
  20. Failure of smooth pasting principle and nonexistence of equilibrium stopping rules under time-inconsistency (2021)
  21. Singular stochastic control and optimal stopping (1987)
  22. Connections between optimal stopping and singular stochastic control I. Monotone follower problems (1984)
  23. Connections between optimal stopping and singular stochastic control (1998)
  24. TABLES OF INTEGRAL TRANSFORMS [Vol 1-2]. (1954)
  25. Risk Aversion in the Small and in the Large (1964)
  26. Aspects of the Theory of Risk Bearing (1965)
  27. Local Time Pushed Mixed Equilibrium Strategies for Time-Inconsistent Stopping Problems (2024)
  28. Equilibrium concepts for time-inconsistent stopping problems in continuous time (2021)
  29. On time-inconsistent stopping problems and mixed strategy stopping times (2020)
  30. On the equilibrium strategies for time-inconsistent problems in continuous time (2021)
  31. Strong and weak equilibria for time-inconsistent stochastic control in continuous time (2021)

0 of 39 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.