Before revision:  We recall the rigorous framework of [ Grasselli, M. R., Lecl\`ere, V. and Ludkovski, M. Priority option : the value of being a leader . Math. and Fin. Econ., 2013]  and extend it to the presence of a random regulator.
After revision:  We recall the rigorous framework of [ Grasselli, M. R., Lecl\`ere, V. and Ludkovski, M. Priority option : the value of being a leader , International Journal of Theoretical and Applied Finance, 16, 2013] and extend it to the presence of a random regulator.