  We investigate a randomization procedure undertaken in real option games
which can serve as a basic model of regulation in a duopoly model of preemptive
investment. We recall the rigorous framework of [M. Grasselli, V. Lecl\`ere and
M. Ludkovsky, Priority Option: the value of being a leader, International
Journal of Theoretical and Applied Finance, 16, 2013], and extend it to a
random regulator. This model generalizes and unifies the different competitive
frameworks proposed in the literature, and creates a new one similar to a
Stackelberg leadership. We fully characterize strategic interactions in the
several situations following from the parametrization of the regulator.
Finally, we study the effect of the coordination game and uncertainty of
outcome when agents are risk-averse, providing new intuitions for the standard
case.
