Product Differentiation and Price Competition between a Safe and a Risky Seller

We consider a market served by a safe and a risky seller. While the expensive safe seller can solve the problems of all consumers, the cheap risky seller can help a consumer only with a certain probability. The risky seller's success probabilities are distributed across consumers, and by the choice of her quality the risky seller determines the shape of this distribution. If the risky seller fails, a consumer ends up with the safe seller, paying for the service twice. We study the price-quality competition between the two providers. We show that the principle of maximum product differentiation does not hold in our model, i.e., the risky seller does not choose the minimum quality level in order to relax price competition