Describe the conflict of the main characters in the story "Thank You Ma'am"

While the main conflict in the story is man v. man, I think a solid argument could be made that there are several examples of man v. self conflicts.

The main source of conflict in the story is man v. man - in other words, this is when two characters (the protagonist and the antagonist) are against each other. In this case, Mrs. Bates and Roger are against each other since Roger attempted to steal Mrs. Bates' purse. The story says, "It was about eleven o’clock at night, and she was walking alone, when a boy ran up behind her and tried to snatch her purse." 

Furthermore, Mrs. Bates is not letting Roger get away with attempting to steal her purse. Instead, she is trying to teach him a moral lesson. This is where I think an argument can be made that there are some examples of man v. self conflicts. When there is a man v. self conflict, a character is struggling morally and may or may not succeed in overcoming that obstacle. 

After Mrs. Bates and Roger make it to her house, Roger struggles with deciding whether he should stay or make a run for it. The text says, "Roger looked at the door—looked at the woman—looked at the door—and went to the sink." This shows a man v. self conflict because since the moment Roger attempted to steal Mrs. Bates purse, he was trying to run away. However, this pivotal moment shows that he is deciding to stay with her instead of running. This demonstrates a change in Roger and his behavior. 

Another subtle example of a man v. self conflict is apparent in the way that Mrs. Bates reveals her intentions to Roger. She says, "I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know..." This shows that Mrs. Bates might see a bit of herself in Roger, and therefore sees a greater need in helping him get back on the right track.