Product differentiation and endogenous mode of competition

There exists a continuum of prices between Bertrand and joint-profit maximization prices which can be interpreted as the outcome of a two-stage game where firms first invest to increase product differentiation and then compete in prices. The lower the costs of differentiating their products from each other the more relaxed competition in the product market and the closer firms will be to the collusive outcome of the one-shot game for given degree of differentiation. The higher the costs the harsher competition in the market and the closer to the Bertrand solution of the one-shot game with given degree of differentiation.