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

A safe and risky seller serve a market. 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; 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. The risky seller chooses a quality-price pair inducing the safe seller to stick to his monopoly strategy. Some but not maximum differentiation results.