Dynamic Effects Arise Due to Consumers' Preferences Depending on Past Choices.

Area of Science:

• Game Theory
• Economic Modeling
• Dynamical Systems

Background:

• Economic agents often exhibit preferences influenced by past decisions.
• Dynamic duopoly models are crucial for understanding market competition.
• Cobb-Douglas utility functions provide a foundational framework for preference analysis.

Purpose of the Study:

• To analyze a dynamic duopoly game with state-dependent preferences.
• To investigate the stability and chaotic dynamics arising from player interactions.
• To establish conditions for predictable and unpredictable market behaviors.

Main Methods:

• Analysis of a one-dimensional logistic map derived from single-player actions.
• Calculation and stability analysis of fixed points for both single- and multi-player cases.
• Numerical simulations and entropy calculations to explore chaotic dynamics.

Main Results:

• The single-player case simplifies to a logistic map, with its fixed points' stability analyzed.
• Conditions for the stability of fixed points in the two-player case are determined by game parameters.
• Numerical simulations confirm chaotic behaviors, with entropy measures quantifying time series regularity.

Conclusions:

• The dynamic duopoly game exhibits complex behaviors, including chaos, depending on player strategies and parameters.
• Stability conditions provide insights into market predictability.
• The study highlights the importance of considering past choices in economic modeling.