We examine the profitability and the welfare implications of price
discrimination in two-sided markets. Platforms have information about
the preferences of the agents that allows them to price discriminate
within each group. The conventional wisdom from one-sided horizontally
differentiated markets is that price discrimination hurts the firms and
benefits consumers, prisoners' dilemma. Moreover, it is well-known that
the presence of indirect externalities in two-sided markets can
intensify the competition. Despite all these, we show that the
possibility of price discrimination, in a two-sided market, may actually
soften the competition. Therefore, the implications of price
discrimination from one-sided markets may not carry over to two-sided
markets. This is the case regardless of whether prices are public or
private, although private prices boost profits. Our analysis also sheds
light on the welfare properties of price discrimination in intermediate
goods markets, such as Business-to-Business (B2B) markets