Bayesian price leadership

Abstract

In this paper, we consider a linear price setting duopoly competition with differentiated goods and with unknown costs. The firms' aims are to choose the prices of their products according to the well-known concept of perfect Bayesian Nash equilibrium. There is a firm (F 1) that chooses first the price p 1 of its good; the other firm (F 2) observes p 1 and then chooses the price p 2 of its good. We suppose that each firm has two different technologies, and uses one of them following a probability distribution. The utilization of one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian Nash equilibrium for this game. We analyze the advantages, for firms and for consumers, of using the technology with highest production cost versus the one with cheapest production cost.