I think every Australian kid played a game like this called French cricket, which is probably a Britishism. If something ie. cricket has been bastardised then the French must have done it. And you could have whatever identity you wanted, as long as your big brother let you.
Two points: If 'bat' = 'cat', then 'cook' = 'book', so don't be surprised if the cook dresses like a librarian.
Also, there are several important identities left unmentioned, e.g.
the Wankster, the Prankster, the Naked Civil Servant, the Devilled Egg, the Wife of Bath, the Minion of Sauron, Extra-Virgin Olive, Alas Poor Yorick, the Steroid-Using Cricketer, the Flapper, the Rapper, Ethel the Quantity-Surveying Aardvark, Much the Miller's Son, Katie the Farmer's Daughter, the Traveling Salesman, Mulder the Fox, the Fettered Ursine, Wittgenstein the Poker, Hillary the Joker, and Herbie the Huckster.
"The object of Hangman's Cricket is for each competitor to retain his allotted nine lives by scoring runs with the 'Cat', or bat, defending his lower leg from being struck by the ball. There is no limit to the number of players as long as each has an identity agreed by the two referees. Each identity has its own characteristic which must be obeyed.
The more important identities are the Emperor, the Widow, the Judge, the Hangman, the Ghost, the Red Queen, the Fat Lady, the Dunce, the Businessmen, the Adulterer, the Harlot, the Gravedigger, the Maiden, the Twins, the Chinaman, the Savage, the Cook, the General, the Prisoner, the Beggarman, the Thief and the Priest."