Adaptivity Gaps in Two-Sided Assortment Optimization

We study a two-sided assortment optimization framework to address the challenge of choice congestion faced by matching platforms. The goal is to decide the assortments to offer to agents in order to maximize the expected number of matches. We identify several classes of policies that the platforms can use in their design. Our main goal is to measure the value that one class of policies have over another one. For this, we define the adaptivity gap as the worst-case ratio between the optimal value achieved by two different policy classes. First, we show that the adaptivity gap between the class of policies that statically show assortments to one-side first and the class of policies that adaptively show assortments to one-side first is exactly \(1-1/e\) . Second, we show that the adaptivity gap between the latter class of policies and the fully adaptive class of policies that show assortments to agents one by one is exactly 1/2. Finally, we observe that the worst policies are those who simultaneously show assortments to all the agents, in fact, we show that the adaptivity gap with respect to one-sided policies can be arbitrarily small. These results showcase the benefit of each class of policies and, in particular, demonstrate that the optimal value of the best class of adaptive policies is a constant multiplicative factor away from those of one-sided policies.