It's not everyday that you get tot receive 1 eth to your wallet and there could be a reason since this is no small amount will try to trace the owner and thank him for sending it to me, and if he says he wants it back and was sent by mistake I will just send the half this is to teach him a lesson that he must always check the address and for the time and effort I spent looking for him.
I quite like your opinion. Actually this is the best way to teach him a lesson and should learn from the next trading sessions because any mistake will cost you money. If it were me, I would do the same for you in this case but I need to know his contact information first as this is the best way to solve any problems.