Imagine a scenario in which a game X installed on your mobile device wants to access your account information from social network Y. Assume that Y exposes some API, and have features like "login with Y" etc. On desktop PC X could popup new browser window, with domain of Y clearly shown in address bar, with a padlock icon clearly indicating SSL connection, and in this popup, social network Y would ask user to provide login, password, and agreement to pass some information (like name, avatar, e-mail) to the application X. For example OAuth 2 uses this approach.
In my opinion, on mobile the situation is in rather different, as application X can take control of whole screen. In particular it can draw on the device's screen something that is indistinguishable from a real browser and hijack login and password provided by user.
How one can combat malicious applications which cover whole screen and pretend to be browsers, or even OS's settings windows etc?