Perpetual leapfrogging in Bertrand duopoly

We consider different patterns of infinite technological adoption choices by firms in a Bertrand duopoly. Every period technological progress provides a sequence of cost reducing innovations. The equilibrium concept is Markov perfect equilibrium. We analyze conditions for which equilibrium adoption leads to persistent leadership and those where firms alternate in adoption inducing leapfrogging. Only leapfrogging leads to technological improvement in the long run. Demand conditions play a crucial role in determining whether leapfrogging can be perpetual in Bertrand duopoly.