Incentives in matching markets: counting and comparing manipulating agents

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. We count the number of agents with an incentive to manipulate and rank mechanisms by their level of manipulability. This ranking sheds a new light on practical design decisions such as the design of the entry-level medical labor market in the US, and school admissions systems in New York, Chicago, Denver and many cities in Ghana and in the UK.