We show that Ergin & Sönmez's (2006) results which show that for schools it is a dominant strategy to truthfully rank the students under the Boston mechanism, and that the Nash equilibrium outcomes in undominated strategies of the induced game are stable, rely crucially on two assumptions....

Manipulability is a threat to the successful design of centralized matching markets. However, in many applications some manipulation is inevitable and the designer wants to compare manipulable mechanisms to select the best among them. We count the number of agents with an incentive to manipulate...