Regret‐free truth‐telling in school choice with consent

Efficiency Adjusted Deferred Acceptance Rule (EDA) is a promising candidate mechanism for a public school assignment. A potential drawback of EDA is that it could encourage students to game the system since it is not strategy‐proof. However, to successfully strategize, students typically need information that is unlikely to be available to them in practice. We model school choice under incomplete information and show that EDA is regret‐free truth‐telling, which is a weaker incentive property than strategy‐proofness and was introduced by Fernandez (2020). We also show that there is no efficient matching rule that weakly Pareto dominates a stable matching rule and is regret‐free truth‐telling. Note that the original version of EDA by Kesten (2010) weakly Pareto dominates a stable matching rule, but it is not efficient.