It seems to be a problem of "desired processes" vs "goals". Picking Martha Monkey up from the station is a goal, while playing outside is a desired process. If one Noddy picks up Martha Monkey from the station, all of the Noddys' desires for Martha to be back from the station are fulfilled. However, if a Noddy plays outside, this only fulfills that Noddy's desire to play outside.
This looks a lot like the "tragedy of the commons" idea so often referred to in economics, when framed in the sense of multiple simultaneous instances of the same person. This is the first time I have really understood how TDT works.
An episode of the Noddy animated series has the following plot.
Noddy needs to go pick up Martha Monkey at the station. But it's such a nice, sunny day that he would prefer to play around outside. He gets an idea to solve this dilemma. He casts a duplication spell on himself and his car and tells the duplicate to go fetch Martha while he goes out to play. Later, Noddy is out having fun when he suddenly spots his duplicate. It turns out that the duplicate also preferred playing outside to doing the errand so he also cast a duplication spell. Then they see another duplicate, and another...
I think this story makes for a nice simple illustration of one of our perennial decision theoretic issues: When making decisions you should take into account that agents identical to yourself will make the same decision in the same situation. A common real-life example of the Noddy problem is when we try to pawn off our dietary problems to our future selves.