The Short-Side Advantage in Random Matching Markets

Theory of and Experiments on Minimally Invasive Stability Preservation in Changing Two-Sided Matching Markets

“…For Delete, the effect was strongest, as deleting a single agent leads to an average normalized symmetric difference of 0.38. For Delete, Ashlagi, Kanoria, and Leshno (2017), Cai and Thomas (2021), Knuth, Motwani, and Pittel (1990) and Pittel (1989) offer some theoretical intuition of this phenomenon: Assuming that agents have random preferences (as in our experiments), with high probability in a men-optimal matching the average rank that a man has for the woman matched to him is log(n) (Knuth, Motwani, and Pittel 1990;Pittel 1989), whereas in an instance with n men and n − 1 women the average rank a man has for the woman matched to him is n 3 log(n) (Ashlagi, Kanoria, and Leshno 2017;Cai and Thomas 2021). Thus, if we delete a single woman from the instance (which happens with 50% probability when we delete a single agent), then already only to realize these average ranks, the given matching needs to be fundamentally restructured.…”