This is an interesting question to consider. Generally, Mansfield is famed for the way in which she depicts the powerless position of women in a patriarchal society, and so this would suggest that the female protagonists of these stories do not exercise power over men.
"The Little Governess" could be used as an example of this. Note the way in which the governess finds herself dependent upon the strange German who shares a carriage with her. In addition, the power that this man has over her is clearly indicated by the kiss that he gives her against her will:
She sprang up but he was too quick and he held her against the wall, pressed against her his hard old body and his twitching knee, and though she shook her head from side to side, distracted, kissed her on the mouth.
The governess is therefore shown to occupy no power over men whatsoever. The physical way in which she is overpowered only serves to underline her general position of weakness and powerlessness.
As for Laura in "The Garden Party," although the story is on the whole absent of male characters, the dead Mr. Scott, when she goes to visit his corpse and pay her respects, seems to exert a particular power over her. It is through looking at his peaceful nature that Laura experiences an epiphany about her life and the garden party:
He was given up to dream. What did garden parties and baskets and lace frocks matter to him? He was far from all those things. He was wonderful, beautiful. While they were laughing and while the band was plahying, this marvel had come to the lane.
Thus, although Laura occupies a higher social class than the Scotts, she is still shown to learn something from the dead Mr. Scott.
Lastly, Leila in "Her First Ball" arguably could be the one female character that shows her power over men through the way in which she is able to forget the fat man's remarks and carry on enjoying her first ball in spite of the threat of mortality. Although initially she is greatly impacted by his words and thoroughly depressed, wanting to go home, as the next dance starts and she begins to whirl around the room, she completely puts the fat man out of her head and therefore shows her power over him. Note how she responds when she sees him again:
And when her next partner bumped her into the fat man and he said, "Perdon," she smiled at him more radiantly than ever. She didn't even recognise him again.
Although initially this fat man is shown to have power over her by the way in which his words upset Leila, she quickly exerts her own power by forgetting him and his speech.