It doesn't work like that unfortunately. Permissions are based solely on the record Owner. There is no way to configure it by Creator.
You've got three options that I can think of:
1. There is an option in the System Settings (General Tab) which may satisfy your needs, called "Share reassigned records with original owner". Itis off by default, but if you turn it on, then all records will be automatically shared with the original owner when they are reassigned.
This will work if a user saves the case in his own name, and then reassigns it to someone else.
However, if the record is initially created with some else set as the owner, then this will not work for you.
2. Depending on your business requirements, you may be able to set up a number of business units and user roles that will satisfy your needs. This would take some thought into how to set it up, and it may impact other areas of your crm
3. Create some custom security. You can open up the security roles for global read access, and use plugins to control visibility based on Creator. This method would be the most difficult to implement, but it can give you exactly the behavior you are looking for.