A New Family of Rules for Probabilistic Assignment Based on Trading Rights and Priorities

Abstract

We consider object allocation problems when rules can select lotteries. We introduce a family of rules indexed by two parameters. The first parameter can be interpreted as the “trading rights” of agents over objects. It determines the amount of each object that each agent has the right to trade. When several agents have positive rights over the same object, a priority order associated with that object specifies who is allowed to trade that object first, second and so on. The second parameter is the profile of priorities attached to objects. Each of our rules is defined by an algorithm similar to Gale’s Top Trading Cycles algorithm (Shapley and Scarf, 1974). Cycles are formed according to this algorithm. In each cycle, agents trade a common probability share of objects. The family includes prominent sd-strategy-proof rules in the literature, such as the Top Trading Cycles rule, the Sequential Priority rules (Svensson, 1999), and the Hierarchical Exchange rules (Papai, 2000). We prove that each of our rules is sd-efficient. We provide a full description of the subclass of our rules that satisfies the sd-endowment lower bound. When there is an agent who has positive shares of two objects, no rule within our family satisfies both the sd-endowment lower bound and sd-strategy proofness. Thus, our paper contributes to the understanding of which social objectives are compatible and which are not.

About the presenter's visit

Dr Acelya Altuntas will be visiting the School of Economics on Tuesday 17^th September 2019.  While here she will be using room 520A Colin Clark Building.  If you would like to meet with her or have lunch or dinner with her please contact Dr Metin Uyanik who will be her host while at The University of Queensland.  Dr  Uyanik can be contacted on m.uyanik@uq.edu.au.