  Flexibility is a cornerstone of operations management, crucial to hedge
stochasticity in product demands, service requirements, and resource
allocation. In two-sided platforms, flexibility is also two-sided and can be
viewed as the compatibility of agents on one side with agents on the other
side. Platform actions often influence the flexibility on either the demand or
the supply side. But how should flexibility be jointly allocated across
different sides? Whereas the literature has traditionally focused on only one
side at a time, our work initiates the study of two-sided flexibility in
matching platforms. We propose a parsimonious matching model in random graphs
and identify the flexibility allocation that optimizes the expected size of a
maximum matching. Our findings reveal that flexibility allocation is a
first-order issue: for a given flexibility budget, the resulting matching size
can vary greatly depending on how the budget is allocated. Moreover, even in
the simple and symmetric settings we study, the quest for the optimal
allocation is complicated. In particular, easy and costly mistakes can be made
if the flexibility decisions on the demand and supply side are optimized
independently (e.g., by two different teams in the company), rather than
jointly. To guide the search for optimal flexibility allocation, we uncover two
effects, flexibility cannibalization, and flexibility abundance, that govern
when the optimal design places the flexibility budget only on one side or
equally on both sides. In doing so we identify the study of two-sided
flexibility as a significant aspect of platform efficiency.
