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There are differences between analogy and allegory, but some would say that allegory is a form of analogy, so if it is an allegory, it would be an analogy.
It is certainly (specifically) an Allegory (the representation of an idea through characters, events, story, narrative). One allegory is Pride: Hauchecorne was ashamed of picking up the string: He made it a point to pretend to be looking for something else when his enemy catches him. No one believes him when he's vindicated. They think he and Paumelle were in on it together. He can't let it go. At this point, his guilt or innocence is not irrelevant, but it is beside A point: that point being that he's more concerned with being thought of as a theif than he is with the truth. He's more concerned with what other people think of him: Pride.
Analogies can be shared relations between two pairs of terms -
arm: hand : : leg: foot
But they can also be shared relations, or shared attributes between two dissimilar (or similar) things. "The Piece of String" is a metaphor for pride (or cynicism: townspeople), Malandain is like a rat (simile). These (metaphor and simile) stand for things they do not directly signify. And although 'analogy' (historically) is a broad term, it is generally thought of as a relationship between two or more things. The relationship is based on a shared meaning, attribute or structure: in this case, analogy is called an extended metaphor.
In literature and science, analogy is often used with respect to form. The parts of one system correspond to the parts of another system. I.e., The oxygen atom is analogous to the solar system. "The Piece of String" is analogous to "The Myth of Sisyphus" in that they're both short fiction and the main characters are facing hopeless situations.
One more thing: The 'piece of string 'itself is analogous to the story itself. In Maupassant's story "The Necklace," he says, "How small a thing is needed to make or ruin us!" The string, in a short story, in the grand scheme of things, is as insignificant as the events (the story). A purse is stolen, somebody gets blamed, and then it's found. Big deal. Hauchecorne makes too much out of it. This is self-reflexive because the story is analogous to a part of itself. And that (analogy) is analogous to the Solar system/atom analogy.
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