One of the differences between market design and the theoretical mechanism design literature is that in mechanism design, the theorist creates the whole universe of strategies available to participants, while in practical market design, the marketplace being designed is part of some larger economic environment, which gives the participants potentially bigger strategy sets.
Here's a paper that takes that point of view with respect to school choice. In the empirical part of the paper, a switch from a manipulable immediate acceptance algorithm to a strategy proof deferred acceptance algorithm influences families with an outside option (a guaranteed continuation in the school where they are enrolled in pre-kindergarten) differently from families without that safe option. When the manipulable algorithm is used, families without an outside option often find it too risky to compete for scarce spaces in the most desirable schools, which they can safely do when the strategy proof algorithm is employed.
Centralized School choice with unequal outside options by Mohammad Akbarpour, Adam Kapor, Christopher Neilson, Winnie van Dijk, Seth Zimmerman, Journal of Public Economics, Volume 210, June 2022, 104644
Abstract: We study how market design choices exacerbate or mitigate pre-existing inequalities among participants. We introduce outside options in a well-known school choice model, and show that students always prefer manipulable over strategy-proof mechanisms if and only if they have an outside option. We test for the proposed relationship between outside options and manipulability in a setting where we can identify students’ outside options and observe applications under two mechanisms. Consistent with theory, students with an outside option are more likely to list popular, highly-rated schools under the Boston mechanism, and this gap disappears after switching to a Deferred Acceptance mechanism.
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Related earlier posts:
Monday, January 28, 2019
And here's a post about a paper that takes outside options seriously from a different point of view.
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