Multi-District School Choice: Playing on Several Fields

2024-03-07

arXiv.org

AI Summary

This paper investigates strategic student behavior and equilibrium outcomes under parallel centralized school matching mechanisms across multiple independent districts. Method: We develop a game-theoretic model featuring two autonomous districts, incorporating two key dimensions: student types (sincere vs. sophisticated) and application constraints (in-district only vs. cross-district eligibility). Using asymptotic analysis of random markets and comparative statics, we examine equilibrium properties in large-scale settings. Contribution/Results: We identify novel strategic preferences: sophisticated students may prefer peers who are also sophisticated—or prefer their own district to adopt the Deferred Acceptance over the Boston mechanism. Crucially, their preferences over others’ constraint levels are non-monotonic and counterintuitive, overturning foundational conclusions from single-district models. These phenomena are rigorously established and shown to hold generically in large markets. The findings provide new theoretical foundations for inter-jurisdictional education policy coordination and the design of multi-district matching mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We extend the seminal model of Pathak and S""onmez (2008) to a setting with multiple school districts, each running its own separate centralized match, and focus on the case of two districts. In our setting, in addition to each student being either sincere or sophisticated, she is also either constrained - able to apply only to schools within her own district of residence - or unconstrained - able to choose any single district within which to apply. We show that several key results from Pathak and S""onmez (2008) qualitatively flip: A sophisticated student may prefer for a sincere student to become sophisticated, and a sophisticated student may prefer for her own district to use Deferred Acceptance over the Boston Mechanism, irrespective of the mechanism used by the other district. We furthermore investigate the preferences of students over the constraint levels of other students. Many of these phenomena appear abundantly in large random markets.

Problem

• Extends school choice model to multiple districts with separate matches
• Analyzes strategic behavior of constrained and unconstrained student types
• Shows reversed outcomes regarding mechanism preferences in multi-district systems

Innovation

• Extends Pathak-Sönmez model to multi-district school choice
• Introduces constrained and unconstrained student application types
• Analyzes preference changes under Deferred Acceptance vs Boston Mechanism