School choice with common preferences and incomplete information admits a winner's curse, by Kloosterman and Troyan

 Suppose that schools have an intrinsic quality that would affect the preferences of all students if they knew it, but some students are better informed than others. Then, for uninformed students, there can be a kind of winner's curse associated with being accepted to a school: the fact that it had seats available suggests that it might not be high quality.  Kloosterman and Troyan propose mitigating this by giving each student a secure school for which he/she has high enough priority to be admitted regardless of others' preferences: " a secure school is one with enough seats for j and every student who has higher priority than j. "  When all students have the same ordinal preferences at every state of the world, then the deferred acceptance algorithm with students proposing continues to make it a dominant strategy for informed students to state their true preferences, and there is an equilibrium that avoids the winners curse in which each uninformed student lists their secure school as their first choice.

School choice with asymmetric information: Priority design and the curse of acceptance

by Andrew Kloosterman and Peter Troyan 

Theoretical Economics, Volume 15, Issue 3, July 2020, Pages: 1095-1133

Abstract: We generalize standard school choice models to allow for interdependent preferences and differentially informed students. We show that, in general, the commonly used deferred acceptance mechanism is no longer strategy‐proof, the outcome is not stable, and may make less informed students worse off. We attribute these results to a curse of acceptance. However, we also show that if priorities are designed appropriately, positive results are recovered: equilibrium strategies are simple, the outcome is stable, and less informed students are protected from the curse of acceptance. Our results have implications for the current debate over priority design in school choice.

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"How do secure schools help the uninformed? The problem for them is the curse of acceptance, and a secure school allows for them to have a default option that they can get in every state. Hence, the curse is entirely eliminated by allowing them to expect to get average utility, rather than always being left with the worst schools in every state. Theorem 1 formalizes this intuition to all markets in the common ordinal preferences model."