Maybe you can have it like this (i don't know if it will be easy or difficult for you)
We make a player and share it
He will have basic info like Name, Nationality, Role, Batting Hand, Bowling Hand, Bowling Style
He will be added to the sim database for all and anyone can download it to their account
Anyone can add as many players as they want to the database but there should not be duplicates
If i want to start my league, i will download the required players to my account and if they are not available, add them to database
Then i will edit the attributes as per requirement, if a player is already used in my previous league, he can have same attributes