Abstract
The authors modify the price-setting version of the vertically differentiated duopoly model by Aoki (Effect of Credible Quality Investment with Bertrand and Cournot Competition, 2003) by introducing an extended game in which firms noncooperatively choose the timing of moves at the quality stage. Their results show that there are multiple equilibria in pure strategies, whereby firms always select sequential play at the quality stage. They also investigate the mixed-strategy equilibrium, revealing that the probability of generating out-of-equilibrium outcomes is higher than its complement to one. In the alternative case with full market coverage, the authors 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.
Highlights
We study the equilibria of a vertically di¤erentiated Bertrand duopoly where the timing of moves at the quality stage is endogenised via an extended game with observable delay à la Hamilton and Slutsky (1990)
This reveals that the quality stage has a unique subgame perfect equilibrium at the intersection of dominant strategies where the Nash and Stackelberg solutions coincide, since best reply functions are orthogonal in that stage
By assuming as exogenous whether a ...rm provides the high or low quality, the best response functions become continuous and ...rms may have the possibility of non cooperatively choosing the respective roles in the quality stage via an extended game with observable delay à la Hamilton and Slutsky (1990)
Summary
We study the equilibria of a vertically di¤erentiated Bertrand duopoly where the timing of moves at the quality stage is endogenised via an extended game with observable delay à la Hamilton and Slutsky (1990). Instead we assume as exogenous the location of ...rms along the quality spectrum, while endogenising the distribution of roles to be taken at the quality stage through a pre-play stage preceding the quality investment phase In this respect, our analysis is based on d’Aspremont and GérardVaret (1980) and Hamilton and Slutsky (1990), according to whom a game is Stackelberg-solvable if there exists a Stackelberg equilibrium that Paretodominates the Nash solution.. We investigate the same issue under full market coverage (not considered by Aoki, 2003) This reveals that the quality stage has a unique subgame perfect equilibrium at the intersection of dominant strategies where the Nash and Stackelberg solutions coincide, since best reply functions are orthogonal in that stage. This implies that, in the presence of full market coverage, the choice of timing becomes immaterial
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