Markovian assignment rules

Abstract

Topics : Economics Theory, Economics generalInternational audienceWe analyze dynamic assignment problems where agents successively receive different objects (positions, offices, etc.). A finite set of n vertically differentiated indivisible objects are assigned to n agents who live n periods. At each period, a new agent enters society, and the oldest agent retires, leaving his object to be reassigned. We define independent assignment rules (where the assignment of an object to an agent is independent of the way other objects are allocated to other agents), efficient assignment rules (where there does not exist another assignment rule with larger expected surplus), and fair assignment rules (where agents experiencing the same circumstances have identical histories in the long run). When agents are homogenous, we characterize efficient, independent and fair rules as generalizations of the seniority rule. When agents draw their types at random, we prove that independence and efficiency are incompatible, and that efficient and fair rules only exist when there are two types of agents. We characterize two simple rules (type-rank and type-seniority) which satisfy both efficiency and fairness criteria in dichotomous settings

A dynamic school choice model

“…Hence, we describe the initial submatching of period 1 as a function ν 1 : I 1 E → S such that ν 1 (i) = s if and only if i is initially matched to school s. For any period t ≥ 2, the initial submatching, denoted by ν t , is defined by the matching of the previous period; that is, given the matching of 3 As it is common in this type of model, we assume that each school's priority ranking is responsive (see Roth and Sotomayor [12] for more details). 4 Although formal notation would be t , to simplify it we will not use the subindex t. Then with we will refer to teacher's preferences in the period under study. 5 The subscript E is motivated by the fact that teachers in this group play the role of what is known in the literature as existing tenants.…”

“…In contrast, there are many real-life applications where an assignment is made in a dynamic context. Some examples are on-campus housing for college students, in which freshmen apply to move in and graduating seniors leave (Kurino [10]), kidney exchange of patients, in which each agent arrives with an object to trade (Ünver [14]), and firms with workers whose entry and exit lead to a reassignment of fixed resources (Bloch and Cantala [4]). In this paper, we study a dynamic version of the well-known school choice model.…”

Optimal assignment of durable objects to successive agents

“…This functional differential equation does not typically admit closed form solutions. 4 Inspection of equation (2) provides additional information on the optimal selectivity function φ:…”

“…Axiomatic characterizations of assignment rules for durable goods have recently been proposed by Kurino (2008) and Bloch and Cantala (2008). Kurino (2008) considers a dynamic extension of Abdulkadiroglu and Sönmez (1999)'s study of house allocation with existing tenants -the first example of an assignment problem with individual rationality constraints -, and analyzes whether the rules proposed in the static paper still satisfy efficiency and incentive compatibility in the dynamic context.…”

“…Kurino (2008) considers a dynamic extension of Abdulkadiroglu and Sönmez (1999)'s study of house allocation with existing tenants -the first example of an assignment problem with individual rationality constraints -, and analyzes whether the rules proposed in the static paper still satisfy efficiency and incentive compatibility in the dynamic context. Bloch and Cantala (2008) consider a model where agents are assigned to different, vertically related objects, and characterize Markovian assignment rules which satisfy myopic efficiency and fairness. By contrast, in this paper, we consider a simpler model where agents only live two periods and can only be assigned one good.…”