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Delayed nonlinear cournot and bertrand dynamics with product differentiation.
Akio Matsumoto1, Ferenc Szidarovszky
1Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo, 192-0393, Japan.
Nonlinear Dynamics, Psychology, and Life Sciences
|June 19, 2007
Summary
This study analyzes dynamic duopolies, finding stable equilibria under normal conditions. However, using delayed information can destabilize market dynamics, highlighting complex firm behaviors in pricing and quantity adjustments.
Area of Science:
- Economics
- Game Theory
- Industrial Organization
Background:
- Understanding market stability is crucial in economic modeling.
- Dynamic duopolies with product differentiation present complex strategic interactions.
- Existing models often assume perfect and immediate information, which may not reflect reality.
Purpose of the Study:
- To analyze the stability of dynamic duopolies with product differentiation.
- To investigate the impact of information delays on market equilibrium stability.
- To explore both price and quantity adjustment mechanisms in these markets.
Main Methods:
- Theoretical analysis to prove local asymptotic stability under realistic conditions.
- Derivation of stability conditions for special cases involving information delays.
- Simulation of dynamic systems to illustrate complex behaviors and outcomes.
Main Results:
- Equilibrium in dynamic duopolies with product differentiation is generally locally asymptotically stable.
- The introduction of delayed information in firms' best responses can lead to instability.
- Simulation results reveal intricate dynamics in both price and quantity adjustment models.
Conclusions:
- Market stability in dynamic duopolies is sensitive to the timeliness of information.
- Firms' strategic choices regarding information processing significantly influence market outcomes.
- The study provides insights into the complex, dynamic nature of oligopolistic markets.
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