Many critics see Act IV, Scene 5 as marking the point of Kate's defeat. In reality, she is not defeated at all. The game which she has played expertly up until the time of her marriage (getting her way through ranting and bullying) has changed and become far more sophisticated. Rather than succumbing to Petruchio's demands, she learns that marriage is built around give and take; it is a compromise. When she chooses to follow the rules, she is rewarded — and so is Petruchio. By humoring Petruchio in his purposely outlandish demands that the sun is the moon, the moon is the sun, and that the old man a young woman, Kate's life runs much more smoothly.
Petruchio, on the other hand, will gladly give Kate anything she desires, as long as she is willing to humor him. In some senses, perhaps, this game gives Petruchio power, but it is power he is willing to share with her. He, too, is glad to compromise once the initial rules are met. Further, he knows Kate has come to understand what he's up to; her good humored and elaborate replies clearly reveal she is willing to play his game and perhaps best him at it, too. Petruchio knows he has an especially wise wife who can match his wit and will if she so desires. In the end, Kate has not lost anything. Rather, a new world has opened to her — an adult world with adult compromises and consequences. Her increased maturity is, in fact, quite becoming.
Vincentio's arrival on the scene moves us toward the play's inevitable intertwining of the primary and secondary plots. With all the disguising which has occurred in the play, Vincentio's arrival isn't totally unexpected. As with all good comedies of mistaken identity, an outsider (or person innocent of