Endogenous Timing in Quality Investments and Price Competition

We modify the price-setting version of the vertically differentiated duopoly model by Aoki (2003) by introducing an extended game in which firms noncooperatively choose the timing of moves at the quality stage. Our results show that there are multiple equilibria in pure strategies, in which firms always select sequential play at the quality stage. We also investigate the mixed-strategy equilibrium, revealing that the probability of generating outcomes out of equilibrium is higher than its complement to one. In the alternative of full market coverage, we show that the quality stage is solved in dominant strategies and therefore the choice of roles becomes irrelevant as the Nash and Stackelberg solutions coincide.