The film "North By Northwest" seems to have two theories of Kaplan's mission.
On the one hand he's supposed to be the agent following Vandamm. This is why it's important to the Professor that Vandamm never discovers Kaplan's fictiveness: he would then realize that Eve is really the agent.
On the other hand Kaplan seems to have an independent life, with travel plans and hotel reservations unrelated to Vandamm's activities, plans and reservations that Vandamm reads to Roger in one scene. So when Roger unknowingly gets on the same train for Chicago as Eve, Leonard and Vandamm, the coincidence is plausible: they are all headed to Chicago to find Kaplan. But in their minds, why did Kaplan make these plans (before the beginning of the film) to go to Chicago, if not to follow them?
Who’s chasing whom?