Strategyproofness-Exposing Descriptions of Matching Mechanisms

A menu description exposes strategyproofness by presenting a mechanism to player i in two steps. Step (1) uses others' reports to describe i's menu of potential outcomes. Step (2) uses i's report to select i's favorite outcome from her menu. We provide novel menu descriptions of the Deferred Acceptance (DA) and Top Trading Cycles (TTC) matching mechanisms. For TTC, our description additionally yields a proof of the strategyproofness of TTC's traditional description, in a way that we prove is impossible for DA.