What are some open problems in mathematical economics which are treated as if they have been solved in economics papers?

As an example, one of my teachers has previously pointed out to me that there is no existence and uniqueness proof of a specific type of Overlapping Generation problem, yet most academics with this specialty write papers that assume that their computed solution is the correct one.

Are there more examples of this sort, in which economists (implicitly) make use of a foundational result, despite no one having proven it?

  • 1
    $\begingroup$ Could you please link an example of an Overlapping Generation paper where the author computes an equilibrium and it is not clearly unique? (I assume existence is clear.) $\endgroup$
    – Giskard
    Aug 22 '18 at 0:18
  • 2
    $\begingroup$ Nobody has proven so far that stationary equilibria in the 1998 Krusell & Smith model exist. I'm pretty sure one could prove existence of $\epsilon$-equilibria though. $\endgroup$ Aug 22 '18 at 16:31

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