Strategic new product pricing when demand obeys saturation effects

We analyze dynamic pricing strategies for new products over an infinite planning horizon in a duopolistic market. The sales dynamic is modelled as a linear demand function with saturation effects, marginal costs are assumed to be constant. The optimal pricing strategies are obtained as (degenerate) closed-loop Nash solutions. It is shown that the optimal dynamic prices are greater than the static ones. In the case of no discounting there is in addition to the constant solution also an equilibrium with monotonically increasing prices.