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Delay Cournot duopoly models revisited.

Luca Guerrini1, Akio Matsumoto2, Ferenc Szidarovszky3

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Time delays in economic models can cause oscillations. This study shows different delay lengths create simple and complex dynamics in Cournot duopoly, with information delay not impacting stability.

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Area of Science:

  • Economics
  • Mathematical Economics
  • Economic Dynamics

Background:

  • Economic phenomena inherently involve time delays.
  • These delays are recognized as potential drivers of oscillatory behavior.
  • Understanding delay effects is crucial for economic modeling.

Purpose of the Study:

  • To investigate the impact of time delays on economic dynamics.
  • To analyze the effects of different delay lengths in Cournot duopoly models.
  • To determine how delays influence stability and generate complex behaviors.

Main Methods:

  • Developed continuous-time Cournot duopoly models with varying delays.
  • Employed analytical methods to examine local dynamics and stability.
  • Utilized numerical simulations to explore global dynamics and complex behaviors.

Main Results:

  • Derived analytical conditions for stability switching.
  • Demonstrated numerically that delay lengths generate simple and complex dynamics.
  • Found that delays in collecting competitor output information do not independently affect stability.

Conclusions:

  • Time delays are significant factors in economic dynamics, capable of inducing oscillations.
  • The length of time delays critically influences the emergence of simple to complex dynamics in Cournot competition.
  • Specific information-gathering delays do not destabilize the Cournot duopoly equilibrium.