Dynamic Matching in Overloaded Waiting Lists

To study waiting-lists as allocation mechanisms, we analyze a class of waiting-list mechanisms where agents are offered a choice among items with corresponding expected waiting times. Because the expected waiting time required for a given item fluctuates over time, different agents may face different waiting times, potentially resulting in misallocation of items. In a stylized model we derive expressions for welfare and compare mechanisms. We find that a simple randomized assignment policy can decrease expected wait fluctuations, thereby reducing misallocation and increasing welfare.

[1]  J. Little A Proof for the Queuing Formula: L = λW , 1961 .

[2]  J D Littler,et al.  A PROOF OF THE QUEUING FORMULA , 1961 .

[3]  P. Naor The Regulation of Queue Size by Levying Tolls , 1969 .

[4]  Y. Barzel A Theory of Rationing by Waiting , 1974, The Journal of Law and Economics.

[5]  De Vany,et al.  Uncertainty, Waiting Time, and Capacity Utilization: A Stochastic Theory of Product Quality , 1976 .

[6]  D. Carlton,et al.  Market Behavior with Demand Uncertainty and Price Inflexibility , 1976 .

[7]  D. Carlton,et al.  Peak-load pricing with stochastic demand , 1977 .

[8]  S. Stidham,et al.  Individual versus Social Optimization in the Allocation of Customers to Alternative Servers , 1983 .

[9]  Edward H. Kaplan,et al.  Managing the demand for public housing , 1984 .

[10]  C. M. Lindsay,et al.  Rationing by waiting lists. , 1984, The American economic review.

[11]  P. Cramton,et al.  Dissolving a Partnership Efficiently , 1985 .

[12]  Edward H. Kaplan,et al.  Tenant Assignment Models , 1986, Oper. Res..

[14]  Edward H. Kaplan,et al.  A PUBLIC HOUSING QUEUE WITH RENEGING , 1988 .

[15]  Eitan Altman,et al.  Individual Equilibrium and Learning in Processor Sharing Systems , 1998, Oper. Res..

[16]  Stefanos A. Zenios,et al.  Modeling the transplant waiting list: A queueing model with reneging , 1999, Queueing Syst. Theory Appl..

[17]  Stephen Martin,et al.  Rationing by waiting lists: an empirical investigation , 1999 .

[18]  Lawrence M. Wein,et al.  Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List , 2000, Oper. Res..

[19]  Vol Cxv Issue EFFICIENT AUCTIONS , 2000 .

[20]  Refael Hassin,et al.  To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems , 2002 .

[21]  D. Bergemann,et al.  Robust Mechanism Design , 2003 .

[22]  R. Wiesner,et al.  Model for end-stage liver disease (MELD) and allocation of donor livers. , 2003, Gastroenterology.

[23]  David M. Kreps,et al.  Relational Incentive Contracts , 2003 .

[24]  Jeffrey C. Ely,et al.  Foundations of Dominant Strategy Mechanisms , 2007 .

[25]  Xuanming Su,et al.  Patient Choice in Kidney Allocation: The Role of the Queueing Discipline , 2004, Manuf. Serv. Oper. Manag..

[26]  Xuanming Su,et al.  Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model , 2005, Oper. Res..

[27]  Xuanming Su,et al.  Recipient Choice Can Address the Efficiency-Equity Trade-off in Kidney Transplantation: A Mechanism Design Model , 2006, Manag. Sci..

[28]  Atila Abdulkadiro,et al.  Dynamic House Allocations , 2007 .

[29]  Andrew J. Schaefer,et al.  Determining the Acceptance of Cadaveric Livers Using an Implicit Model of the Waiting List , 2007, Oper. Res..

[30]  M. Utku Ünver,et al.  Dynamic Kidney Exchange , 2007 .

[31]  G. Jung,et al.  Model for end-stage liver disease , 2008, Der Chirurg.

[32]  Morimitsu Kurino,et al.  House allocation with overlapping agents: A dynamic mechanism design approach , 2009 .

[33]  Gideon Weiss,et al.  Fcfs infinite bipartite matching of servers and customers , 2009, Advances in Applied Probability.

[34]  Alexander Frankel,et al.  Aligned Delegation , 2010 .

[35]  D. Bergemann,et al.  DYNAMIC AUCTIONS , 2010 .

[36]  Benny Moldovanu,et al.  Efficient sequential assignment with incomplete information , 2010, Games Econ. Behav..

[37]  Morimitsu Kurino House allocation with overlapping generations , 2011 .

[38]  Daniel Monte,et al.  The Daycare Assignment Problem , 2011 .

[39]  Gideon Weiss,et al.  Exact FCFS Matching Rates for Two Infinite Multitype Sequences , 2012, Oper. Res..

[40]  A. Israni,et al.  The kidney allocation system. , 2013, The Surgical clinics of North America.

[41]  Mohammad Akbarpour,et al.  Dynamic matching market design , 2014, EC.

[42]  A. Ichino,et al.  Time Allocation and Task Juggling , 2014 .

[43]  Allan Collard-Wexler,et al.  Dynamic Inputs and Resource (Mis)Allocation , 2014, Journal of Political Economy.

[44]  Daniel Monte,et al.  The Day Care Assignment: A Dynamic Matching Problem , 2014 .

[45]  Judd B. Kessler,et al.  Getting More Organs for Transplantation. , 2014, The American economic review.

[46]  Francis Bloch,et al.  Dynamic Allocation of Objects to Queuing Agents: The Discrete Model , 2014 .

[47]  Sanmay Das,et al.  Competing Dynamic Matching Markets , 2015, AMMA 2015.

[48]  Brendan Lucier,et al.  Non-Optimal Mechanism Design , 2015 .

[49]  Itai Ashlagi,et al.  A dynamic model of barter exchange , 2015, SODA.

[50]  Gabriel D. Carroll Robustness and Linear Contracts , 2015 .

[51]  Laura Doval A Theory of Stability in Dynamic Matching Markets , 2015 .

[52]  On Matching and Thickness in Heterogeneous Dynamic Markets , 2016, EC.

[53]  Daniel Fershtman Matching Auctions: Experimentation and Cross-Subsidization∗ , 2016 .

[54]  Benjamin A. Brooks,et al.  Informationally Robust Optimal Auction Design , 2016 .

[55]  Nick Arnosti,et al.  Design of Lotteries and Waitlists for Affordable Housing Allocation , 2017 .

[56]  Francis Bloch,et al.  Dynamic Assignment of Objects to Queuing Agents , 2017 .

[57]  W. Dijk,et al.  The socio-economic consequences of housing assistance , 2018 .

[58]  On the Efficiency of Queueing in Dynamic Matching Markets , 2019 .

[59]  Leeat Yariv,et al.  Optimal dynamic matching , 2020 .

[60]  Daniel Waldinger,et al.  Targeting In-Kind Transfers through Market Design: A Revealed Preference Analysis of Public Housing Allocation , 2021 .

[61]  Carson J. Reeling,et al.  Welfare effects of dynamic matching: An empirical analysis , 2021, The Review of Economic Studies.

[62]  James Schummer,et al.  Influencing waiting lists , 2021, J. Econ. Theory.