Generic regularity of differentiated product oligopolies - Michael Zierhut (Economic Theory, 2020)
In oligopoly models with differentiated products, producers face a market demand function that reflects the preferences of consumers. However, typical assumptions on preferences place only weak restrictions on the shape of aggregate demand. This may result in profit functions that are not strictly quasiconcave, in best-reply correspondences that are not differentiable, and in equilibria that are not robust to perturbations. This paper establishes differentiability and robustness as a generic property: for an open, dense set of economies, best replies are differentiable in a neighborhood of equilibria, which is a precondition for comparative statics. All these economies have a finite number of equilibria in pure strategies.
Keywords: D43; D50; D51; 330; Comparative statics; Imperfect competition; Cournot–Walras equilibrium; Regular production economy