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  • 1Economics and Management Department, Yuncheng University, Fudan West, Yuncheng, 044000, Shanxi, China. byuang@163.com.

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Summary
This summary is machine-generated.

This study introduces a random Bertrand model with Brownian motion to analyze dynamic pricing strategies. It reveals that firms inefficient at error management, especially smaller ones, face higher failure risks in fluctuating markets.

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Area of Science:

  • Economics
  • Mathematical Economics
  • Game Theory

Background:

  • The Bertrand model is a foundational economic model for price competition.
  • Dynamic pricing in changing economic environments requires models that account for uncertainty and managerial behavior.
  • Managerial error avoidance in dynamic price settings is crucial for market stability.

Purpose of the Study:

  • To extend the Bertrand model to incorporate stochastic elements using Brownian motion.
  • To analyze the equilibrium of a dynamic stochastic game model.
  • To investigate the impact of error management efficiency and market share on organizational failure.

Main Methods:

  • Extension of the Bertrand model with Brownian motion.
  • Analysis of a stochastic game model.
  • Solution using Hamilton-Jacobi-Bellman equations.
  • Numerical simulation to observe equilibrium dynamics.

Main Results:

  • The stochastic game model's equilibrium was solved using Hamilton-Jacobi-Bellman equations.
  • Numerical simulations showed equilibrium fluctuations, with a constant value also observed.
  • The model demonstrates that less efficient error management increases failure susceptibility.

Conclusions:

  • Organizations with lower efficiency in managing errors, particularly those with smaller market shares, are more vulnerable to failure.
  • The extended Bertrand model provides insights into dynamic pricing and market competition under uncertainty.
  • The findings highlight the importance of robust error management strategies for business resilience.