Obviously Strategy-Proof Multi-Dimensional Allocation and the Value of Choice
Quitzé Valenzuela-Stookey
TL;DR
This paper studies how a principal should allocate heterogeneous tasks when agents’ task preferences are private and each agent can demand a status-quo assignment. It shows that, under mild conditions, allowing choice through trading mechanisms can improve the social cost, and that this value of choice persists even when limited to obviously strategy-proof (OSP) mechanisms. The author fully characterizes OSP trading mechanisms as polarized-ray structures, establishing a dimension-reducing, robust design space with ex-post optimal polarized-ray (EOPR) mechanisms. A large-market relaxation yields a dual formulation that is tractable and proves asymptotic optimality as the market grows, providing a principled path to selecting among OSP candidates. The results offer a practical framework for designing fair, simple, and robust allocation rules in high-dimensional matching problems.
Abstract
A principal must allocate a set of heterogeneous tasks (or objects) among multiple agents. The principal has preferences over the allocation. Each agent has preferences over which tasks they are assigned, which are their private information. The principal is constrained by the fact that each agent has the right to demand some status-quo task assignment. I characterize the conditions under which the principal can gain by delegating some control over the assignment to the agents. Within a large class of delegation mechanisms, I then characterize those that are obviously strategy-proof (OSP), and provide guidance for choosing among OSP mechanisms.