Mechanisms for a dynamic many-to-many school choice problem

2024-11-12

AI Summary

This paper studies dynamic school assignment mechanisms for tenured faculty under multi-institutional employment constraints. Addressing the dual constraints of school priority orderings and path-independent faculty choice behavior, we introduce the novel concept of “dynamic stability.” We propose the Tenure-Respecting Dynamic Assignment (TRDA) mechanism, which achieves constrained-optimal matching while respecting tenure rights and minimizing unreasonable claims. Building upon TRDA, we design the Tenure-Respecting Efficient and Adaptive Dynamic Assignment (TREADA) mechanism, which strictly Pareto-dominates all dynamically stable matchings and attains global efficiency when all faculty consent. We prove the universal existence of dynamically stable matchings and characterize conditions under which dynamic manipulation is non-explicit. Integrating insights from game theory, matching theory, and dynamic mechanism design, our framework delivers a general solution for educational human resource allocation that simultaneously ensures fairness, efficiency, and practical feasibility.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We examine the problem of assigning teachers to public schools over time when teachers have tenured positions and can work simultaneously in multiple schools. To do this, we investigate a dynamic many-to-many school choice problem where public schools have priorities over teachers and teachers hold path-independent choice functions selecting subsets of schools. We introduce a new concept of dynamic stability that recognizes the tenured positions of teachers and we prove that a dynamically stable matching always exists. We propose the Tenure-Respecting Deferred Acceptance (TRDA) mechanism, which produces a dynamically stable matching that is constrained-efficient within the class of dynamically stable matchings and minimizes unjustified claims. To improve efficiency beyond this class, we also propose the Tenure-Respecting Efficiency-Adjusted Deferred Acceptance (TREADA) mechanism, an adaptation of the Efficiency-Adjusted Deferred Acceptance mechanism to our dynamic context. We demonstrate that the outcome of the TREADA mechanism Pareto-dominates any dynamically stable matching and achieves efficiency when all teachers consent. Additionally, we examine the issue of manipulability, showing that although the TRDA and TREADA mechanisms can be manipulated, they remain non-obviously dynamically manipulable under specific conditions on schools' priorities.

Problem

• Dynamic teacher-school assignment with tenure and multiple schools
• Ensuring stable matching respecting teachers' tenured positions
• Improving efficiency while minimizing unjustified claims

Innovation

• Dynamic stability concept for teacher-school matching
• Tenure-Respecting Deferred Acceptance (TRDA) mechanism
• Efficiency-Adjusted Deferred Acceptance (TREADA) mechanism