Sub directory login

Hi,

I have more than one website under subdirectory of main domain.
Can users automatically log in to subdirectory wordpress sites when they log in to the main directory wordpress site ?

For example;
I have an http://www.example.com wordpress website and http://www.example.com/stage wordpress websites.
One of my user logged in http://www.example.com with social account and then open url of http://www.example.com/stage.
Is it possible to login automatically with main session cookie ?