Regret-Free Truth-Telling in School Choice with Consent

The Efficiency Adjusted Deferred Acceptance Matching Rule (EDA) is a promising candidate mechanism for 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 Pareto dominates a stable matching rule and is regret-free truth-telling.