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Two-sided matching platforms provide users with menus of matchrecommendations. To maximize the number of realized matches between the twosides (referred here as customers and suppliers), the platform must balance theinherent tension between recommending customers more potential suppliers tomatch with and avoiding potential collisions. We introduce a stylized model tostudy the above trade-off. The platform offers each customer a menu ofsuppliers, and customers choose, simultaneously and independently, either asupplier from their menu or to remain unmatched. Suppliers then see the set ofcustomers that have selected them, and choose to either match with one of thesecustomers or to remain unmatched. A match occurs if a customer and a supplierchoose each other (in sequence). Agents' choices are probabilistic, andproportional to public scores of agents in their menu and a score that isassociated with remaining unmatched. The platform's problem is to constructmenus for costumers to maximize the number of matches. This problem is shown tobe strongly NP-hard via a reduction from 3-partition. We provide an efficientalgorithm that achieves a constant-factor approximation to the expected numberof matches.

Assortment planning for two-sided sequential matching markets