We examine the profitability and the welfare implications of pricediscrimination in two-sided markets. Platforms have information aboutthe preferences of the agents that allows them to price discriminatewithin each group. The conventional wisdom from one-sided horizontallydifferentiated markets is that price discrimination hurts the firms andbenefits consumers, prisoners' dilemma. Moreover, it is well-known thatthe presence of indirect externalities in two-sided markets canintensify the competition. Despite all these, we show that thepossibility of price discrimination, in a two-sided market, may actuallysoften the competition. Therefore, the implications of pricediscrimination from one-sided markets may not carry over to two-sidedmarkets. This is the case regardless of whether prices are public orprivate, although private prices boost profits. Our analysis also shedslight on the welfare properties of price discrimination in intermediategoods markets, such as Business-to-Business (B2B) markets.