Sequential product positioning and entry timing under differential costs in a continuous-time model

We investigate the product positioning decisions of two firms that enter a market sequentially under a duopoly competition. Two important assumptions are made: differential marginal production costs between the two firms, and endogenous entry timing of a follower in a continuous-time setting. We analyze a standard location-pricing Hotelling game with quadratic transportation costs with the points of departure being that the two firms (i) are allowed to have different (constant) marginal costs; (ii) enter sequentially in a pre-determined order in a market in which the consumers are growing over time; and (iii) are not restricted to choosing positions inside the interval in which consumer preferences are located. For the first mover, the dynamic market growth can give rise to a trade-off between exploiting short-run monopoly and long-run duopoly profits. This trade-off affects the equilibrium positions when the first mover has a larger marginal cost as well as a larger discount rate, in which case the first mover chooses its position at the center of the interval along which consumers are located. We also introduce uncertainty regarding entry and marginal costs to examine their effects on positioning and entry timing. If the entry cost of the follower firm is uncertain for the leader firm, then the leader firm is likely to choose its position farther away from the most attractive point. Moreover, we show that the follower firm enters the market earlier if the leader firm faces such uncertainty.