Dynamic Assignment of Objects to Queuing Agents

Abstract

We analyze the dynamic assignment of objects to agents organized in a constant size waiting list. Applications include the assignment of social housing and organs for transplants. We analyze the optimal design of probabilistic queuing disciplines, punishment schemes, and information release. With private values, all agents prefer first-come first-served to the lottery, but waste is lower at the lottery. With common values, all agents prefer first-come first-served to any other mechanism, and waste is minimized at the lottery. Punishment schemes accelerate turnover in the queue and information release increases the value of agents at the top of the waiting list. (JEL C78, D44, D82)

Dynamic Incentives in Wait List Mechanisms

“…Arnosti and Shi (2017) also find that FCFS produces higher match value than LM. Indeed, Bloch and Cantala (2017) show that FCFS yields better match value than any mechanism that gives agents that have waited longer weakly higher priority. However, this result depends on the nature of primitives as shown in Leshno (2017), who studies a model with agents that have preferences for a specific type of object.…”

“…While the design of such systems has garnered significant research attention, most theoretical results yield answers that depend on the primitives of the market (compare Su and Zenios 2004;Leshno 2017;Bloch and Cantala 2017). Moreover, the state of the art empirical methods used to prospectively evaluate wait list designs do not incorporate the dynamic incentives that are central to the theoretical literature.…”

“…We consider a model similar to the one described in Bloch and Cantala (2017). There are n ≥ k agents waiting for an object, where k is a positive constant.…”

Matching through institutions

“…In the school choice context, a number of recent papers have analyzed the effect of constraints resulting from affirmative action considerations. One stream of papers interprets affirmative action as "leveling the playing field", as in Kojima (2012) Finally, we note that the assignment of social housing that motivated our study has recently been analyzed in a series of papers (Leshno (2014), Bloch and Cantala (2016), Schummer (2016) and Thakral (2015)) which focus on very different aspects of the problem -the revelation of persistent information on types in Leshno (2014), the dynamic sequence of decisions in Bloch and Cantala (2016), the manipulation of orders in Schummer (2015) and multiple waiting list mechanisms in Thakral (2015).…”

Gradual College Admission

“…Literature With respect to the existing literature, gradual matching problems differ substantially from dynamic matching problems, which generally consist of situations where participants, and thus matching opportunities, arrive sequentially, and/or where agents may "consume" different matches at different periods. Dynamic problems with irreversible matches can be found in Doval (2019), Baccara et al (2019), Bloch and Cantala (2017) or Akbarpour et al (2018). Models with limited commitment, i.e., where agents can be matched multiple times across periods are studied by Kadam and Kotowski (2018a,b), Kotowski (2019), Kennes et al (2014Kennes et al ( , 2019 and Pereyra (2013).…”