Learning Strategies in Decentralized Matching Markets under Uncertain Preferences

We study two-sided decentralized matching markets in which participants have uncertain preferences. We present a statistical model to learn the preferences. The model incorporates uncertain state and the participants' competition on one side of the market. We derive an optimal strategy that maximizes the agent's expected payoff and calibrate the uncertain state by taking the opportunity costs into account. We discuss the sense in which the matching derived from the proposed strategy has a stability property. We also prove a fairness property that asserts that there exists no justified envy according to the proposed strategy. We provide numerical results to demonstrate the improved payoff, stability and fairness, compared to alternative methods.

[1]  SangMok Lee,et al.  Incentive Compatibility of Large Centralized Matching Markets , 2017 .

[2]  A. Siow,et al.  Who Marries Whom and Why , 2006, Journal of Political Economy.

[3]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[4]  Itai Ashlagi,et al.  Communication Requirements and Informative Signaling in Matching Markets , 2017, EC.

[5]  Michael I. Jordan,et al.  Competing Bandits in Matching Markets , 2019, AISTATS.

[6]  D. Ruppert.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

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

[8]  Sanmay Das,et al.  Two-Sided Bandits and the Dating Market , 2005, IJCAI.

[9]  G. Wahba,et al.  Smoothing spline ANOVA for exponential families, with application to the Wisconsin Epidemiological Study of Diabetic Retinopathy : the 1994 Neyman Memorial Lecture , 1995 .

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

[11]  Jonathan Levin,et al.  Early Admissions at Selective Colleges , 2009 .

[12]  Antonio Romero-Medina,et al.  Simple Mechanisms to Implement the Core of College Admissions Problems , 2000, Games Econ. Behav..

[13]  A. Roth,et al.  New physicians: a natural experiment in market organization , 1990, Science.

[14]  Yi Lin.  Tensor product space ANOVA models in multivariate function estimation , 1998 .

[15]  M. Balinski,et al.  A Tale of Two Mechanisms: Student Placement , 1999 .

[16]  Guillaume Haeringer,et al.  Decentralized job matching , 2011, Int. J. Game Theory.

[17]  Pierre-André Chiappori,et al.  The Econometrics of Matching Models , 2016 .

[18]  Donald E. Knuth,et al.  Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms , 1996 .

[19]  Alvin E. Roth.  Deferred acceptance algorithms: history, theory, practice, and open questions , 2008, Int. J. Game Theory.

[20]  Lorenzo Rosasco,et al.  Generalization Properties of Learning with Random Features , 2016, NIPS.

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

[22]  J. Schreiber.  Foundations Of Statistics , 2016 .

[23]  A. Roth.  The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.

[24]  A. Roth,et al.  Turnaround Time and Bottlenecks in Market Clearing: Decentralized Matching in the Market for Clinical Psychologists , 1997, Journal of Political Economy.

[25]  Yeon-Koo Che,et al.  Decentralized College Admissions , 2016, Journal of Political Economy.

[26]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[27]  Konrad Menzel.  Large Matching Markets as Two‐Sided Demand Systems , 2015 .

[28]  Lones Smith,et al.  Student Portfolios and the College Admissions Problem , 2013 .

[29]  Larry Samuelson,et al.  Stable Matching with Incomplete Information (Second Version) , 2012 .

[30]  Emir Kamenica,et al.  Gender Differences in Mate Selection: Evidence From a Speed Dating Experiment , 2006 .

[31]  Hector Chade,et al.  Simultaneous Search , 2006 .

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

[33]  G. Wahba,et al.  Some results on Tchebycheffian spline functions , 1971 .

[34]  Chao Fu,et al.  Equilibrium Tuition, Applications, Admissions and Enrollment in the College Market , 2012 .

[35]  Eduardo M. Azevedo,et al.  A Supply and Demand Framework for Two-Sided Matching Markets , 2014, Journal of Political Economy.

[36]  Richard J. Zeckhauser,et al.  The Early Admissions Game: Joining the Elite , 2004 .

[37]  Dennis Epple,et al.  Admission, Tuition, and Financial Aid Policies in the Market for Higher Education , 2006 .

[38]  Benjamin Recht,et al.  Random Features for Large-Scale Kernel Machines , 2007, NIPS.

[39]  G. Wahba.  Support vector machines, reproducing kernel Hilbert spaces, and randomized GACV , 1999 .

[40]  Sébastien Bubeck,et al.  Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems , 2012, Found. Trends Mach. Learn..

[41]  Isa Emin Hafalir,et al.  College admissions with entrance exams: Centralized versus decentralized , 2018, J. Econ. Theory.