Matching and price competition: would personalized prices help?

We analyze the generalized deferred-acceptance algorithm when preferences are known with an error. This algorithm incorporates personalized salaries and is considered as a replacement for the current algorithm for National Resident Matching Program (NRMP). Maintaining Bulow and Levin's (in Am Econ Rev 96(3):652-668, 2006) assumption on preferences, we show that an error in preferences of a worker propagates through the algorithm, leading to a change in the salary of every more productive worker. Thus, relatively small individual errors accumulate toward the top and may lead to highly distorted salaries for top workers the same way as mild compression translates into highly compressed salaries on the top in the Bulow and Levin study of the current NRMP algorithm.