Besides the Induction and the obvious physical disguises (costumes, if you will), we can also see Shakespeare calling attention to his play as just that, a play, through the characters of Kate and Petruchio. Rather than seeing them as the shrew and the tamer, we can also see them as analogous to an actor and a director. In very literal terms, the character of Kate is created by a young man playing a woman who creates a shrewish persona for herself so she can more easily deal with the world around her (largely through avoiding it). When her disguise is no longer useful to her (or when the director, Petruchio, has finally convinced her to abandon the disguise) she assumes another role — this time the dutiful wife (thinking of Kate as an actress also helps with interpreting her speech in Act V, Scene 2).
Petruchio is the director who orchestrates the production we see before us. He theorizes on how to get Kate to do what he wishes and begins planning his performance early. Although the staging of Petruchio's performance starts at the wedding when he assumes the costume of a wild man, he stages his largest production when he vows to kill his wife with kindness. In helping Katherine to a more mature state of being, Petruchio dictates all the particulars, just as a director dictates a production. He runs the show, so to speak, governing when his wife will enter and exit, when she will eat and sleep, when the action will advance and when it will repeat itself, and even attempts to oversee time itself. He very carefully sets up the elaborate production at hand, helping move his shrewish wife into desirable mate.
Disguising and role playing of all sorts fill the scenes of The Taming of the Shrew. In addition to advancing the general plot, the pervasive disguising and metadramatic nature of the play suggest that role players abound and that, as wary spectators, we must be like Petruchio, careful not to take things at face value because we are surrounded by duplicitousness.
