Theoretical Economics, Volume 16, Number 3 (July 2021)

Theoretical Economics 16 (2021), 853–879

When is a monotone function cyclically monotone?

Alexey I. Kushnir, Lev V. Lokutsievskiy


We provide sufficient conditions for a monotone function with a finite set of outcomes to be cyclically monotone. Using these conditions, we show that any monotone function defined on the domain of gross substitutes is cyclically monotone. The result also extends to the domain of generalized gross substitutes and complements.

Keywords: Monotone, cyclically monotone, non-convex domain, gross substitutes, gross substitutes and complements, mechanism design, algebraic topology, homology, nerve theorem

JEL classification: D82

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