Modeling a differentiated goods bertrand duopoly under uncertain demand

Abstract

This thesis explores the design of information structures in a Bertrand duopoly with differentiated products under demand uncertainty. Specifically, we consider a setting in which two firms compete in prices while facing a common uncertain demand parameter, which we modeled as a random variable over the unit interval. Drawing inspiration from the framework of Bayesian persuasion, we examine how posterior beliefs, induced through noisy signals, affect equilibrium payoffs. By comparing the expected profits under prior and posterior beliefs, we show—using Jensen’s inequality — that firms achieve strictly higher expected payoffs under the prior belief than under the posterior when the governing interaction terms lie in a certain interval. This result illustrates that more precise information can be strategically disadvantageous in a Bayesian game with continuous action and type spaces. Furthermore, we extend this finding to an n-player symmetric setting, where we discover that the aforementioned interval shrinks as the number of competing firms increases. These insights contribute to a deeper understanding regarding the role and value of private information in oligopoly pricing games.