Price Competition with the Attraction Demand Model: Existence of Unique Equilibrium and Its Stability
研究了在吸引力需求模型和凸成本假设下，伯特兰寡头价格竞争博弈中纳什均衡的存在性、唯一性和全局稳定性，并保证了试错过程的线性收敛速度。
We show the existence of Nash equilibria in a Bertrand oligopoly price competition game using a possibly asymmetric attraction demand model with convex costs under mild assumptions. We show that the equilibrium is unique and globally stable. To our knowledge, this is the first paper to show the existence of a unique equilibrium with both nonlinear demand and nonlinear costs. In addition, we guarantee the linear convergence rate of tatônnement. We illustrate the applicability of this approach with several examples arising from operational considerations that are often ignored in the economics literature.