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On the Equivalence of Weak- and Cyclic-Monotonicity

We provide an approach to studying the equivalence of weak- and cyclic-monotonicity conditions in convex and non-convex domains with a finite set of outcomes. Using this approach, we establish the new equivalence results for gross-substitutes preferences and single-peaked preferences on posets. We also provide novel applications of the equivalence result to problems in mechanism design, spatial allocation, revealed preference theory, and producer choice theory.