Strategyproofness-Exposing Mechanism Descriptions

A menu description defines a mechanism to player $i$ in two steps. Step (1) uses the reports of other players to describe $i$'s menu: the set of $i$'s potential outcomes. Step (2) uses $i$'s report to select $i$'s favorite outcome from her menu. Can menu descriptions better expose strategyproofness, without sacrificing simplicity? We propose a new, simple menu description of Deferred Acceptance. We prove that -- in contrast with other common matching mechanisms -- this menu description must differ substantially from the corresponding traditional description. We demonstrate, with a lab experiment on two simple mechanisms, the promise and challenges of menu descriptions.