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