Using cookies to verify visitors

I"ve been playing a game on-line which requires a password, cookies and javascript in order to play. The problem we have had here is that some players have created multi-accounts to cheat. The admin claims he deletes any multi-accounts, and any accounts with same IP. He also assures us he uses the other info from the cookies to check out any users we feel are cheats in case they use a proxy to change IP. At his request I have from time to time checked him by creating other accounts using not only anonymous proxies, and logging in as a different user on my pc, but by changing my screen resolution etc.. to throw him off. He constantly is able to detect them and delete them.
The problem is there are several accounts that I know for sure are multi-accounts, yet they don't seem to get deleted.
My question is could these other accounts actually have a way of fooling his verification(and if so how can I prove it to him) or is he merely deleting only the accounts he chooses to, thereby favoring one side?

How about simply having 2 or more different computers on seperate ip addresses? This could be especially easy on dial-ups that don't monitor a single account holder logging into 2 or more modems in their bank, remotely accessing another computer, etc... This way they would be using seperate ip address, seperate cookies, seperate monitors, seperate everything, yet be the same person.

It's also not necessarily a good idea to ban multiple accounts from the same IP address. Many institutions (particulary those in educational sectors) have a gateway/proxy to the internet with a single IP address. Each request over HTTP is forwarded by the proxy, so the site that someone is visiting will only see the one main IP address, rather than the ones used for internal network purposes. Stop multiple accounts from the same IP address and you effectively limit such places to only one person being allowed to sign up for the service.