Expectations, network effects and platform pricing

In markets with network effects, users must form expectations about the total number of users who join a given platform. In this paper, we distinguish two ways in which rational expectations can be formed, which correspond to two different types of users-sophisticated and unsophisticated. Only sophisticated users adjust their expectations in response to platforms' price changes. We study the effect of the fraction of sophisticated users on platform profits. A monopoly platform's profits are always increasing in the fraction of sophisticated users. The profits of competing platforms in a market of fixed size are decreasing in the fraction of sophisticated users. When market expansion is introduced, the fraction of sophisticated users that maximizes competing platforms' profits may be positive and is strictly lower than 1. We also investigate the possibility of platforms investing in "educating" unsophisticated users. In a competitive environment, such education is a public good among platforms and therefore the equilibrium level is lower than the one that would maximize joint industry profits.