Better way to write this function

[Gribouillis]

You could try code like

winner = ["nobody", "computer", "player"][(self.computer_choice - self.player_choice) % 3]

It can be made even shorter by using negative indexes in Python list (still assuming computer_choice and player_choice are in (0, 1, 2))

winner = ["nobody", "computer", "player"][self.computer_choice - self.player_choice]