In my community, every user should only have one account.
So I need a solution to verify that the specific account is the only one the user owns
Address the exact scenario that you're saying is a problem.
Keep track of the expected/fair trade value of players and prevent blatantly lope-sided trades, esp. for new accounts. Assume the vast majority of users in your system are non-cheaters.
You can also do things like trickle in funds/points for non-trading actions/automatically overtime, etc.