Android : Identifying Android user

The Google In-App Billing API documentations says:

You should pass in a string token that helps your application to identify the user who made the purchase, so that you can later verify that this is a legitimate purchase by that user. For consumable items, you can use a randomly generated string, but for non-consumable items you should use a string that uniquely identifies the user.

So how do I identify the user? I don't need the username or email, but I need something that will be the same on all devices that have the same Google account registered in the Play Store app and (with high probability) different on devices that don't.

The application does not do anything for which the user would need account, so asking user to log in to the application would be totally silly.