arXiv subjects

Andrew Tai

Publications and source records attributed to Andrew Tai.

5 recordsLinked to original sources

arXiv2026

Random Matching with Minimums

We study stochastic object assignment problems in which objects may have minimum and maximum requirements, such as with classes with upper and lower enrollment bounds. We construct a new random assignment mechanism, the minimums probabilistic serial (MPS) mechanism, which generalizes the Probabilistic Serial mechanism of Bogomolnaia and Moulin (2001). The random allocation produced by MPS is guaranteed to be Pareto efficient; that is, there is no other implementable allocation that all agents prefer via first order stochastic dominance. We also show that MPS is i) envy-free, in that no agent will strictly prefer another agent's assignment, and ii) weak strategyproof, in that agents cannot achieve a better assignment by misreporting their preferences.

econ.TH↗

arXiv2026

Energy-Efficient Collaborative Transport of Tether-Suspended Payloads via Rotating Equilibrium

Collaborative aerial transportation of tethered payloads is fundamentally limited by space, power, and weight constraints. Conventional approaches rely on static equilibrium conditions, where each vehicle tilts to generate the forces that ensure they maintain a formation geometry that avoids aerodynamic interactions and collision. This horizontal thrust component represents a significant energy penalty compared to the ideal case in which each vehicle produces purely vertical thrust to lift the payload. Operating in tighter tether configurations can minimize this effect, but at the cost of either having to fly the vehicles in closer proximity, which risks collision, or significantly increasing the length of the tether, which increases complexity and reduces potential use-cases. We propose operating the tether-suspended flying system at a rotating equilibrium. By maintaining steady circular motion, centrifugal forces provide the necessary horizontal tether tension, allowing each quadrotor to generate purely vertical thrust and thus reducing the total force (and power) required compared to an equilibrium where the thrusts are not vertical. It also allows for a wider range of tether configurations to be used without sacrificing efficiency. Results demonstrate that rotating equilibria can reduce power consumption relative to static lifting by up to 20%, making collaborative aerial solutions more practically relevant.

cs.RO↗

arXiv2025

Shapley-Scarf Markets with Objective Indifferences

Top trading cycles with fixed tie-breaking (TTC) has been suggested to deal with indifferences in object allocation problems. Unfortunately, under general indifferences, TTC is neither Pareto efficient nor group strategy-proof. Furthermore, it may not select an allocation in the core of the market, even when the core is non-empty. However, when indifferences are agreed upon by all agents (``objective indifferences''), TTC maintains Pareto efficiency, group strategy-proofness, and core selection. Further, we characterize objective indifferences as the most general setting where TTC maintains these properties.

econ.TH↗

arXiv2023

House-Swapping with Objective Indifferences

We study the classic house-swapping problem of Shapley and Scarf (1974) in a setting where agents may have "objective" indifferences, i.e., indifferences that are shared by all agents. In other words, if any one agent is indifferent between two houses, then all agents are indifferent between those two houses. The most direct interpretation is the presence of multiple copies of the same object. Our setting is a special case of the house-swapping problem with general indifferences. We derive a simple, easily interpretable algorithm that produces the unique strict core allocation of the house-swapping market, if it exists. Our algorithm runs in square polynomial time, a substantial improvement over the cubed time methods for the more general problem.

econ.TH↗

arXiv2022

Revealed Preferences of One-Sided Matching

This paper finds the testable implications of the core in an exchange economy with unit demand when agents' preferences are unobserved. To do so, I develop a model of aggregate matchings in which the core is falsifiable; the identifying assumption is that agents' preferences are solely determined by observable characteristics. I find conditions that characterize when observed economies are compatible with the core. These conditions are meaningful, intuitive, and tractable, providing a nonparametric test for the core in the style of revealed preferences.

econ.TH↗