Irreversible Investment under Competition with a Markov Switching Regime

In this paper, we study an investment problem in which two asymmetric firms face competition and the regime characterizing economic conditions follows Markov switching. We derive the value functions and investment thresholds of a leader and a follower. One of the interesting results is that in contrast to the case of no regime switching, even if the current market size is small, both advantaged and disadvantaged firms have an incentive to become a leader in some parameter settings.