In the Taming of the Shrew, Petruchio recognizes, respects and desires Kate's intelligence and strength of character. He does not want to conquer or truly tame her. He is a man who is very confident in himself and does not want or need someone to massage his ego. Petruchio seems to me to be a man of sport and challenge and likes to surround himself with witty, challenging people. He wants in a mate what Kate has - fire. From Petruchio's response to his friend Hortensio (I.ii.64-75), it might be said that Petruchio came to Padua to make himself richer by marriage, to any woman, no matter how wretched. Petruchio is not in desperate need of mone