Efficiency and Stability Trade-offs in School Choice: Implementing and Characterizing Nash Equilibria
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2023
- handle: 10670/1.mvjmql
- hal: hal-04238849
http://hal.archives-ouvertes.fr/licences/copyright/ , info:eu-repo/semantics/OpenAccess
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School choice Matching Pareto efficiency Nash equilibrium Deferred acceptance JEL Classification: C78, D47, D50, D82.Sujets proches
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Cyril Rouault, « Efficiency and Stability Trade-offs in School Choice: Implementing and Characterizing Nash Equilibria », HAL-SHS : économie et finance, ID : 10670/1.mvjmql
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We explore the school choice problem and examine assignments that Pareto-dominate the student-optimal stable assignment. Utilizing a strategic approach grounded in Nash equilibria, we highlight the connection between stability and Nash equilibria which result in assignments that enhance student allocations through the deferred acceptance mechanism (DA). We demonstrate that for certain assignments, there exists no Nash equilibrium under DA that leads to these enhanced assignments. We identify a strategy profile for a given assignment, enabling determination of whether a Nash equilibrium exists that leads to this assignment. Then, we characterize strategy profiles that are Nash equilibria and lead to assignments of the efficiency adjusted deferred acceptance mechanism (EADA) introduced by \cite{kesten2010school}. Furthermore, we demonstrate that for each round of EADA, the considered matching can be achieved with a Nash equilibrium using DA.