The real options approach studies an investment problem in which the value of an investment opportunity is uncertain in the future and the cost of investment is somewhat irreversible. As Dixit and Pindyck (1994) point out, studying investment under competition is becoming important, not only because it enables us to analyze a more realistic situation, but also because competition is becoming fierce as a result of a globalizing economy and worldwide deregulation. In this background, many theoretical studies construct models with multiple firms in a real options framework to study the investment problem under competition. Among them, Grenadier (1996) is regarded as a pioneering paper. He models a real estate market with two firms using a real options framework and claims that his model explains a US construction boom in the 1990s. Other important theoretical papers include Huisman and Kort (1999) and Nielsen (2002). Pawlina and Kort (2006) consider the case where two firms are asymmetric in their irreversible costs and present some theoretical results. Their model has three patterns of equilibrium: preemptive, sequential and simultaneous equilibria. Takashima et al. (2008) investigate an electricity market in which two firms are asymmetric in cost parameters and operating options. Kijima and Shibata (2005) and Bouis et al. (2009) extend these approaches to the framework of three or more symmetric firms. Nishide and Yagi (2016) introduce policy uncertainty to the preemption game. As seen above, the literature on real options in competitive environments is very extensive. For a more detailed literature review see, for example, ChevalierRoignanta et al. (2011); Huisman et al. (2004) and Azevedo and Paxson (2014). From another viewpoint, several studies introduce regime uncertainty within a real options analysis to capture economic cycles. As we observed in the global financial crisis after the failure of Lehman Brothers in September 2008, a change in regime can have a significant impact on economic circumstances. One example is the dislocations in the foreign exchange (FX) swap market between the US dollar and three major European currencies, which is empirically reported by Baba and Packer (2009). They report that almost all FX swap deviates from the covered interest rate parity after the Lehman failure, indicating a big effect caused by the change of economic conditions. Theoretical papers that assume regime shifts within a real options framework include Chapter 9 of Dixit and Pindyck (1994); Guo et al. (2005); Hassett and Metcalf (1999); Pawlina and Kort (2005), and Nishide and Nomi (2009). Typically, regime uncertainty is modeled with parameters that describe the dynamics of the state variables following a Markov switching process. Among them, Driffill et al. (2013) study the investment decisions of a project with Markov-modulated geometric Brownian motions. They derive a simultaneous ordinary differential equation system that can calculate an investment threshold for each regime. Their main finding is that Markov switching risk causes a delay in the expected timing of the investment.