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An Experiment on Pareto-Efficiency and Communication in the Gale-Shapley School Choice Mechanism Amy Hall University of Mississippi

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An Experiment on Pareto-Efficiency and Communication in the Gale-Shapley School Choice Mechanism Amy Hall University of Mississippi University of Mississippi eGrove Honors College (Sally McDonnell Barksdale Honors Theses Honors College) 2017 An Experiment on Pareto-Efficiency and Communication in the Gale-Shapley School Choice Mechanism Amy Hall University of Mississippi. Sally McDonnell Barksdale Honors College Follow this and additional works at: https://egrove.olemiss.edu/hon_thesis Part of the Economics Commons Recommended Citation Hall, Amy, "An Experiment on Pareto-Efficiency and Communication in the Gale-Shapley School Choice Mechanism" (2017). Honors Theses. 60. https://egrove.olemiss.edu/hon_thesis/60 This Undergraduate Thesis is brought to you for free and open access by the Honors College (Sally McDonnell Barksdale Honors College) at eGrove. It has been accepted for inclusion in Honors Theses by an authorized administrator of eGrove. For more information, please contact [email protected]. AN EXPERIMENT ON PARETO-EFFICIENCY AND COMMUNICATION IN THE GALE-SHAPLEY SCHOOL CHOICE MECHANISM by Amy Virginia Hall A thesis submitted in partial fulfillment of the requirements of the Sally McDonnell Barksdale Honors College Oxford May 2017 Approved by _________________________________ Advisor: Professor Mark Van Boening _________________________________ Reader: Professor Jody Holland _________________________________ Reader: Professor Melissa Bass © 2017 Amy Virginia Hall ALL RIGHTS RESERVED ii ACKOWLEDGMENTS This experiment would not have been possible without the generous funding from both the Sally McDonnell Barksdale Honors College and the Trent Lott Leadership Institute at The University of Mississippi. I am grateful for their financial support, which covered the costs of this research. I am extremely grateful to my advisor and professor, Dr. Mark Van Boening, for the many hours he spent working with me, as well as his patience and input throughout this entire process. Thank you for sparking my interest in experimental economics and for guiding me through the completion of my own experiment. I would also like to thank Alex Vasios-Sivvopooulos for the hours he spent re-writing the z-tree program used in this experiment and the many occasions on which he aided me in the Mississippi Experimental Research Lab. Finally, I would like to thank Dr. Yan Chen, Professor in the School of Information at the University of Michigan, not only for her extensive research in this field, but also for providing me with the Boston mechanism z-tree program used in her former experiment. iii ABSTRACT AMY VIRGINIA HALL: An Experiment on Pareto-efficiency and Communication in the Gale-Shapley School Choice Mechanism (Under the Direction of Dr. Mark Van Boening) The past few decades have seen an increase in the debate and discussion of school choice, and recent literature has focused on mechanism design approaches to satisfy that choice. The literature includes experimental studies of these mechanisms. I conduct an experiment that examines the Gale-Shapley mechanism. This mechanism considers the rankings by parents and students of their preferred schools as well as the schools’ priorities for students (based primarily on district or walk-zones) and uses a unique algorithm to produce student-school matchings. My experimental design is based primarily on that of “Chinese College Admissions and School Choice Reforms: An Experimental Study” (Chen and Kesten, 2016). I specifically attempt to answer a question raised in their findings about tacit coordination between participants to reach an unstable Pareto-efficient equilibrium. I allow experienced subjects to communicate during the experiment via electronic chat. I am interested in seeing if this communication can facilitate explicit coordination and consistently achieve this Pareto-efficient outcome. I find that experience combined with the chat feature do not seem to significantly affect participants’ ability to coordinate towards the Pareto-efficient outcome, and consistently reaching this outcome is difficult to facilitate. iv Table of Contents List of Tables .................................................................................................................... vii List of Figures .................................................................................................................. viii I. Introduction ...................................................................................................................1 I. A. Overview ................................................................................................................. 1 I. B. Boston mechanism .................................................................................................. 2 I. C. Gale-Shapley mechanism ........................................................................................ 2 I. D. Pareto-efficiency and Justified Envy ...................................................................... 3 II. Literature Review .........................................................................................................4 III. Experimental Design ...................................................................................................8 III. A. Sessions and Protocol ........................................................................................... 8 III. B. Theory and Treatment ........................................................................................ 11 IV. Experimental Results ................................................................................................14 IV. A. Baseline Sessions ............................................................................................... 14 IV. A. 1. Baseline Session 1 ..................................................................................... 15 IV. A. 2. Baseline Session 2 ..................................................................................... 16 IV. A. 3. Baseline Session 3 ..................................................................................... 17 IV. A. 4. Baseline Session 4 ..................................................................................... 18 IV. B. Treatment Sessions ............................................................................................. 18 IV. B. 1. Treatment Cohort A ................................................................................... 18 IV. B. 2. Treatment Cohort B ................................................................................... 21 IV. B. 3. Summary of Treatment Results .................................................................. 24 V. Conclusion .................................................................................................................25 v V. A. Summary ............................................................................................................. 25 V. B. Policy Theory Application ................................................................................. 26 V. C. Limitations .......................................................................................................... 27 References ..........................................................................................................................29 Appendices .........................................................................................................................30 Appendix A: Recruitment Script .................................................................................. 30 Appendix B: Instructions for the Econ Game ............................................................... 31 Appendix C: Baseline Session Results ......................................................................... 39 Appendix D: Special Announcement ............................................................................ 40 Appendix E: Treatment Cohort A Session Results ....................................................... 41 Appendix F: Treatment Cohort B Session Results ....................................................... 42 Appendix G: Session 5x Chat ....................................................................................... 43 Appendix H: Session 8xx Chat ..................................................................................... 44 Appendix I: Session 6x Chat ......................................................................................... 51 Appendix J: Session 7x Chat ........................................................................................ 52 vi List of Tables Table 1. Summary of Current Literature ............................................................................. 7 Table 2. Session Schedule ................................................................................................... 9 Table 3. Payoff .................................................................................................................. 12 Table 4. Summary of Relevant Outcomes ........................................................................ 13 Table 5. Baseline Session Summary ................................................................................. 15 Table 6. Cohort A Session Summary ................................................................................ 21 Table 7. Cohort B Session Summary ................................................................................ 24 Appendix Table C8. Baseline Session Results ................................................................. 39 Appendix Table E9. Treatment Cohort A Session Results ..............................................
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