bzzzzzdroid actually wants to have different permissions for different users.
Creating groups (as marioxcc proposed) seems the way to go.
A special permission that may be worth knowing is the "sticky bit":
$ chmod +t /home/shared
It aims to allow the users to edit/remove their own files in the directory
but not the files owned by another user. It is famously used for /tmp (notice
the "t" at the end of the permissions):
$ ls -l / | grep tmp
drwxrwxrwt 8 root root 4096 janv. 10 10:17 tmp
Obviously, the sticky bit must not be used if the shared directory is a
co-working directory, where files must be modifiable by any user in the
group.