Learning the Demand Function in a Repeated Cournot Oligopoly Game

Abstract

In this article, single product Cournot oligopolies are considered, where the demand and cost functions are linear. While cost functions are completely known by all firms, they only partially know the demand function, as they misspecify the slope. At any stage of the repeated oligopoly game firms update the slope of their subjective demand functions on the basis of the discrepancy they observe between the expected price, computed according to believed demand, and the price they actually observe. This adjustment process has a unique steady state, where any subjective demand function coincides with the true demand function. If such steady state is stable, then the true slope of the demand function can be learned by all oligopolists, even if they start from misspecified initial guesses. Sufficient conditions for the stability of the steady state are given for n-firms oligopolies. In the particular case of a duopoly, an exact delimitation of the stability region in the parameters' space is given, and with the help of numerical simulations, the size and the shape of the basins of attraction is analysed, as well as the kinds of attracting sets that characterise the long-run dynamics of the learning process when the steady state is unstable.