Incentive for adoption of new technology in duopoly under absolute and relative profit maximization

We present an analysis about adoption of new technology by firms in a duopoly with differentiated goods under absolute and relative profit maximization. Technology itself is free, but each firm must expend a fixed set-up cost, for example, for education of its staff. Under absolute profit maximization there are three types of sub-game perfect equilibria depending on the value of set-up cost. Both firms, or one firm, or no firm adopt new technology. On the other hand, under relative profit maximization there are two sub-game perfect equilibria. Both firms or no firm adopt new technology. And we show that if demand is sufficiently high, it is more probable that both firms adopt new technology under relative profit maximization than that both firms, or one firm adopt new technology under absolute profit maximization.