TITLE: Helly's theorem in other areas of mathematics
QUESTION [8 upvotes]: Are there some outstanding results using some version of Helly's theorem in a totally different area (whatever that means) than convex geometry?

REPLY [5 votes]: Helly's theorem plays a role in economics theory and in game theory
(noncooperative games):


Fuchs-Seliger, Susanne. "An application of Helly's theorem to preference-generated choice correspondences." International Economic Review (1984): 71-77.
  (Jstor link.)
Raghavan, T. E. S. "Zero-sum two-person games." Handbook of Game Theory 2 (1994): 735-768. (PDF download.)