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Auctions and Assignment

Paper Session

Friday, Jan. 5, 2024 2:30 PM - 4:30 PM (CST)

Grand Hyatt, Travis A
Hosted By: Econometric Society
  • Chair: Charles Z. Zheng, University of Western Ontario

Adaptive Priority Mechanisms

Oguzhan Celebi
,
Massachusetts Institute of Technology
Joel Peter Flynn
,
Massachusetts Institute of Technology

Abstract

How should authorities that care about match quality and diversity allocate resources when they are uncertain of the market they face? We propose a new class of adaptive priority mechanisms (APM) that prioritize agents as a function of both scores (reflecting match quality) and the socioeconomic characteristics of the assigned agents (reflecting diversity). For a single authority with separable preferences over scores and characteristics, we derive an APM that is optimal, generates a unique outcome, and depends solely on the authority's preferences. By contrast, the ubiquitous priority and quota mechanisms are optimal if and only if the authority is risk-neutral or extremely risk-averse over diversity, respectively. With many authorities, it is dominant for each of them to use the optimal APM, and each so doing implements the unique stable matching. Using data from Chicago Public Schools, we benchmark the gains from adopting APM and find that they may be considerable.

Undergraduate Course Allocation through Competitive Markets

Daniel Kornbluth
,
Carnegie Mellon University
Alexey Kushnir
,
Carnegie Mellon University

Abstract

We consider the problem of allocating courses to students in post-secondary institutions. We propose a mechanism that assigns course seats based on student preferences and respects course priorities. This mechanism uses fake money and competitive equilibrium to allocate courses without transfers and has desirable theoretical properties in terms of stability, efficiency, fairness, and strategy-proofness. In simulations drawing from real-world university data, we demonstrate that its outcomes improve student mean utility and allocation fairness over the outcomes of several celebrated mechanisms currently used in practice.

A Method to Characterize Reduced-Form Auctions

Charles Z. Zheng
,
University of Western Ontario

Abstract

An important problem in mechanism design, characterizing the interim allocations that are the reduced forms of ex post feasible allocations is to replace the ex post feasibility constraints by their interim counterparts. This paper proposes a method to obtain the characterization in models with multiple objects, possibly unit-demand preferences, and arbitrary distributions of types. Any allocation that is about to violate some ex post feasibility constraint can be viewed as a choice function among interim states. From this choice function I derive a family of partial revealed preferences, each rationalizing the choice within a subset of interim states. The upper or lower contour sets of interim states with respect to these partial revealed preferences are then proved to constitute the interim constraints one of which the allocation is about to violate. The method applies easily to generalize the received result in the mainstream model (paramodularity) and establish a counterpart to a contemporary result (total unimodularity), and it applies nontrivially to the assignment problems between N (at least two) objects and two bidders each of whom can have any number of types.
JEL Classifications
  • D4 - Market Structure, Pricing, and Design
  • J3 - Wages, Compensation, and Labor Costs