(Timing product release) Two firms are developing competing products for a market of fixed size….

(Timing product release) Two firms are developing competing products for a market of fixed size. The longer a firm spends on development, the better its product. But the first firm to release its product has an advantage: the customers it obtains will not subsequently switch to its rival. (Once a person starts using a product, the cost of switching to an alternative, even one significantly better, is too high to make a switch worthwhile.) A firm that releases its product first, at time t, captures the share h(t) of the market, where h is a function that increases from time 0 to time T, with h(0) = 0 and h(T) = 1. The remaining market share is left for the other firm. If the firms release their products at the same time, each obtains half of the market. Each firm wishes to obtain the highest possible market share. Model this situation as a strategic game and find its Nash equilibrium (equilibria?). (When finding firm i’s best response to firm j’s release time tj, there are three cases: that in which h(tj) j) = ½ , and that in which h(tj) > ½ .)