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.

翻译：菜单描述通过两个步骤向参与者$i$呈现机制，从而揭示策略可证性。步骤（1）利用其他参与者的报告描述$i$的潜在结果菜单；步骤（2）利用$i$的报告从其菜单中选择其最偏好的结果。我们为延迟接受（DA）与顶级交易圈（TTC）匹配机制提供了新颖的菜单描述。对于TTC，我们的描述进一步证明了其传统描述具有策略可证性，而这种方式我们证明对DA而言是不可能的。