Dynamics Game of Regional Monopolies with Spillovers and Delays

This chapter proposes a dynamic game of two regional monopolies in the same industry. It contains two special features: spillovers and time delays. Other than the usual profit maximization through a linear price function in its region, one regional monopoly experiences a cost-increasing spillover associated with the presence of the other regional monopoly. Each regional monopoly needs time to produce output and to acquire information on spillovers. It is demonstrated first that the production delay can be a source of the birth of cyclic oscillations via a Hopf bifurcation. Second, stability loss and gain repeatedly occur according to the relative magnitude between the production and information delays. The number of the regional monopolies is limited to 2 only for analytical simplicity and will be increased to be more than 3 in a future study.