What does the repeated use of the word "sport" suggest about Antony and Cleopatra's relationship?

Both Antony and Cleopatra describe their relationship as "sport" throughout the play; suggesting that they both view their feelings towards each other as nothing more than something to enjoy. It also suggests a high level of physicality, and even competition, which can be related to their actions throughout the play as powerful and manipulative leaders of opposing sides. Furthermore, the mutual consideration of the relationship as "sport" suggests a strong similarity between the two characters, and thus the sense that they are ideal partners for each other.