Markov Perfect Equilibria in Multi-mode Differential Games with Endogenous Timing of Mode Transitions

In this paper we study Markov-perfect equilibria (MPE) of two-player multi-mode differential games with controlled state dynamics, where one player controls the transition between modes. Different types MPE are characterized distinguishing delay equilibria, inducing for some initial conditions mode switches after a positive finite delay, and now or never under which, depending on condition, switch occurs immediately never. These results applied to analyze game capturing dynamic interaction two incumbent firms among which has decide when extend its product range by introducing new product. The market appeal can be (positively negatively) influenced over time competing through costly investments. It is shown that wide introduction costs equilibrium co-exists continuum each them different introduction.