Matching in the Large: An Experimental Study

Market size has been predicted to play an influential role in a broad class of environments. We study performance of the Boston and the Deferred Acceptance (DA) mechanism in a laboratory where we increase the market size. Our results show that increasing the market size from 4 to 40 students per match increases participant truth-telling under the DA but decreases it under the Boston mechanism, leading to a decrease in efficiency for both mechanisms but no change in the large stability advantage of the DA over the Boston mechanism. We then further increase the market size to 4,000 by introducing robots. When humans play truthful robots (without strategic uncertainty), we find that scale has no effect on best response behavior. However, when humans play empirical robots (with strategic uncertainty), scale increases best responses under both mechanisms, which is likely due to the increase in the precision of subjects’ beliefs about others’ strategies.

[1]  Fuhito Kojima,et al.  Incentives in the probabilistic serial mechanism , 2010, J. Econ. Theory.

[2]  D. J. Roberts,et al.  THE INCENTIVES FOR PRICE-TAKING BEHAVIOR IN LARGE EXCHANGE ECONOMIES , 1976 .

[3]  A. Roth.  The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics , 2002 .

[4]  Yan Chen,et al.  Chinese College Admissions and School Choice Reforms: Theory and Experiments , 2014 .

[5]  Thomas A. Gresik,et al.  The rate at which a simple market converges to efficiency as the number of traders increases: An asymptotic result for optimal trading mechanisms , 1989 .

[6]  Yeon-Koo Che,et al.  Efficient assignment with interdependent values , 2015, J. Econ. Theory.

[7]  Atila Abdulkadiroglu,et al.  School Choice: A Mechanism Design Approach , 2003 .

[8]  U. Fischbacher.  z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[9]  Eduardo M. Azevedo.  Complementarity and Multidimensional Heterogeneity in Matching Markets , 2012 .

[10]  Parag A. Pathak,et al.  Changing the Boston School Choice Mechanism , 2006 .

[11]  Thierry Magnac,et al.  Gaming the Boston School Choice Mechanism in Beijing , 2012 .

[12]  J. Kagel,et al.  The Dynamics of Reorganization in Matching Markets: A Laboratory Experiment Motivated by a Natural Experiment , 2000 .

[13]  Alvin E. Roth,et al.  Pairwise Kidney Exchange , 2004, J. Econ. Theory.

[14]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

[15]  Parag A. Pathak,et al.  School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation , 2011 .

[16]  Jeroen M. Swinkels.  Efficiency of Large Private Value Auctions , 2001 .

[17]  Eduardo M. Azevedo,et al.  Complementarity and Multidimensional Heterogeneity in Large Matching Markets , 2013 .

[18]  M. Utku Ünver,et al.  Efficient Kidney Exchange: Coincidence of Wants in a Markets with Compatibility-Based Preferences , 2009 .

[19]  Yan Chen,et al.  School Choice : An Experimental Study ∗ , 2004 .

[20]  Tayfun Sönmez,et al.  Games of school choice under the Boston mechanism , 2006 .

[21]  Yan Chen,et al.  An experimental study of house allocation mechanisms , 2004 .

[22]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[23]  Parag A. Pathak,et al.  The New York City High School Match , 2005 .

[24]  Itai Ashlagi,et al.  Individual rationality and participation in large scale, multi-hospital kidney exchange , 2011, EC '11.

[25]  J. Hatfield.  Promoting School Competition Through School Choice: A Market Design Approach∗ , 2011 .

[26]  Clayton R. Featherstone,et al.  Improving on Strategy-proof School Choice Mechanisms: An Experimental Investigation I , 2014 .

[27]  J. Pais,et al.  Preference intensities and risk aversion in school choice: a laboratory experiment , 2010, Experimental Economics.

[28]  Joana Pais,et al.  School choice and information: An experimental study on matching mechanisms , 2008, Games Econ. Behav..

[29]  Parag A. Pathak,et al.  Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match , 2009 .

[30]  Drew Fudenberg,et al.  Existence of Equilibrium in Large Double Auctions , 2004, J. Econ. Theory.

[31]  Steven R. Williams,et al.  Convergence to Efficiency in a Simple Market with Incomplete Information , 1994 .

[32]  Jeroen M. Swinkels,et al.  EFFICIENCY OF LARGE DOUBLE AUCTIONS , 2003 .

[33]  Parag A. Pathak,et al.  The Boston Public School Match , 2005 .

[34]  Yan Chen,et al.  Multi-object auctions with package bidding: An experimental comparison of Vickrey and iBEA , 2010, Games Econ. Behav..

[35]  J. Kagel,et al.  Behavior in Multi-Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions * , 2001 .

[36]  Parag A. Pathak,et al.  Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism , 2008 .

[37]  Alvin E. Roth,et al.  The Economics of Matching: Stability and Incentives , 1982, Math. Oper. Res..

[38]  Andrew Schotter,et al.  Matching and chatting: An experimental study of the impact of network communication on school-matching mechanisms , 2017, Games Econ. Behav..

[39]  Itai Ashlagi,et al.  Matching with couples revisited , 2010, EC '11.

[40]  Elena Katok,et al.  Do Auctioneers Pick Optimal Reserve Prices? , 2011, Manag. Sci..

[41]  Caterina Calsamiglia,et al.  Constrained School Choice: An Experimental Study , 2009 .

[42]  Nicole Immorlica,et al.  Marriage, honesty, and stability , 2005, SODA '05.

[43]  Jeroen M. Swinkels,et al.  Efficiency and Information Aggregation in Auctions , 2000 .

[44]  C. Ai,et al.  Interaction terms in logit and probit models , 2003 .

[45]  Paul J Ferraro,et al.  The Source and Significance of Confusion in Public Goods Experiments , 2010 .

[46]  Parag A. Pathak,et al.  Matching with Couples: Stability and Incentives in Large Markets , 2010 .

[47]  A. Roth,et al.  Unraveling Reduces Mobility in a Labor Market: Gastroenterology with and without a Centralized Match , 2003, Journal of Political Economy.

[48]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[49]  Tingting Ding,et al.  Learning and Mechanism Design: An Experimental Test of School Matching Mechanisms with Intergenerational Advice , 2019, The Economic Journal.

[50]  David A. Freedman,et al.  Machiavelli and the Gale-Shapley Algorithm , 1981 .

[51]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[52]  Yan Chen,et al.  Improving Efficiency of On-Campus Housing: An Experimental Study , 2002 .

[53]  Parag A. Pathak,et al.  Appendix to "Incentives and Stability in Large Two-Sided Matching Markets" , 2009 .