Independent serial for each foreign key value
You can't do this with SERIAL.

You could create a SEQUENCE for each owner_id but that'd be painful and scale poorly.

Instead, use a counter table where each owner_id has a separate counter, and 

update players_per_user_counter 
set next_val = next_val + 1 
where player_id = $1 
returning next_val


to get new identifiers. For more info search for "PostgreSQL gapless sequence".

See:


https://stackoverflow.com/q/9984196/398670