The dynamics of Bertrand price competition with cost-reducing investments

We extend the classic Bertrand duopoly model of price competition to a dynamic setting where competing duopolists invest in a stochastically improving production technology to “leapfrog” their rival and attain temporary low‐cost leadership. We find a huge multiplicity of Markov‐perfect equilibria (MPE) and show that when firms move simultaneously the set of all MPE payoffs is a triangle that includes monopoly payoffs and a symmetric zero mixed strategy payoff. When firms move asynchronously, the set of MPE payoffs is strictly within this triangle, but there still is a vast multiplicity of MPE, most of which involve leapfrogging.The authors would like to acknowledge the funding received from the Danish Council for Independent Research and Innovation Fund Denmark. Fedor Iskhakov gratefully acknowledges the support from the Australian Research Council projects CE110001029 and FL110100247 as well as from Frisch Centre project 1307 financed by the Ministry of Labor, Norwa