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
We have implemented this by hiding the registration form. Our customers only see the login form where we use their mobile number as username and send the password by text message.
The backend systems match the mobile number to our master customer database which enforces that the mobile number is unique.
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.
I know this is probably nothing you have expected, but...
My suggestion would be to discourage people from creating another account by offering some bonus values if they use the same account for a longer period, a kind of loyalty program. For some reason using a new account gives some advantages. Let's eliminate them. There are a lot of smart people here, so if you share more details on the advantages someone could come up with some idea. I am fully convinced this is on-topic on SO though.
I think 1 account per email address should be good enough for your needs. After all, account verification doesn't have to end right after signup.
You can publish the IP address of the computer each message was posted from to help your users detect when someone is using multiple accounts from the same computer, and you can use a ranking system to discourage people from using temporary accounts.
Here is an idea:
After that write a program interface for your game masters that:
I do not think you should solve that problem by preventing people having two or more accounts. This is not possible and ineffective. Make it easier to find that evil activities and (automatically temporarly) ban these people.
It's impossible to accomplish this with a program.
The closest you can do is to check the ip address. But it can change, and proxies exist.
Then you could get the computer MAC address, but a network card can be changed. And a computer too.
Then, there is one way to do this, but you need to see the people face to face. Hand them a piece of paper with a unique code. They can only subscribe if they have the code.