The "Batocio" is known for being Harlequin's short wooden club. Kind of tool for carrying out his work as a Zanni (from which Harlequin originates, in Bergamo).
The Zanni were known as "facchini" (porters) people doing a very heavy menial job, lower level in the social scale.
The batocio in Harlequin's hands becomes a stage prop, something that may be used in different ways, from mixing up the polenta, as a knife or a spoon, the rare times he is actually eating (or dreaming of).
Sometimes the batocio becomes a sword or a bat, for hitting other characters, fighting with the Zanni, for instance, using it as a club or a dagger.
The stage batocio was made of two strips of wood, and used as a slapstick, a special effects prop, after all, being able to convey to the public the blows which were given around and to give action and exaggeration to the scene it was used in.
There are two versions of the original use of the batocio:
I would tend to accept the first one, though.