arXiv subjects

Will Sandholtz

Publications and source records attributed to Will Sandholtz.

3 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↗

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↗