What was the problem in "After Twenty Years" by O. Henry? How did the main characters resolve it?

The main problem in the story "After Twenty Years" is Jimmy's. He keeps his appointment to meet his old friend Bob but quickly realizes Bob is a criminal wanted by the Chicago police. Jimmy has to decide between whether (1) to identify himself as a cop and arrest Bob, (2) to identify himself as a cop and warn Bob to get lost, (3) not to identify himself at all and just go away and leave Bob waiting there until he gives up and leaves, or (4) not to identify himself but to get another cop to make the arrest. Jimmy makes the decides to take the fourth option, as shown by the note he leaves for Bob and by the fact that a plainclothes detective arrives to place Bob under arrest.

It is interesting that Jimmy and Bob have a long conversation in the doorway of the hardware store but the reader never suspects Jimmy is experiencing any problem at all. Jimmy's problem shapes the story and determines its outcome. Many readers have questioned whether Jimmy did the right thing. After all, Bob was an old friend—or was he? Bob used to be a friend. It could be argued their friendship ends when Bob lights his cigar and Jimmy sees the face of the man wanted by the Chicago police. Now Bob is an erstwhile friend. Jimmy does not hesitate to decide Bob should be arrested. His only misgiving is about making the arrest himself. He knows this would create an unpleasant scene. Bob would appeal to their old friendship.