arXiv subjects

Joseph Root

Publications and source records attributed to Joseph Root.

8 recordsLinked to original sources

arXiv2026

How to Beat FCFS

We study two observable queues with identical service rates, serving agents who arrive stochastically over time. Agents join the queue that minimizes their expected waiting time. Assuming one queue uses the ubiquitous First-Come-First-Served (FCFS) service rule, we show that by simply modifying its service order, the other queue can capture a strict majority of the demand. We establish an upper bound on the arrival share any rule can capture against FCFS. When both queues can design their service order, we show a novel variant of Last-Come-First-Served (LCFS) is an equilibrium in a low congestion regime. Without commitment, the picture changes, and there is an equilibrium where both queues use FCFS, and agents route to the queue with the shorter waitlist.

econ.TH↗

arXiv2026

A Theory of Network Games Part 1: Utility Representations

We provide interpretable axiomatic foundations for utilities used in network games and identify several principled generalizations. First, we demonstrate that a ubiquitous feature of network games, bilateral strategic interactions, is equivalent to having player utilities that are additively separable across opponents. Common utilities based on a linear aggregate of opponent actions are strategically equivalent to additively separable utilities. Moreover, assuming real-valued actions, we show that a constant rate of substitution between opponents implies a utility that is linear in opponent actions. Finally, we identify precise conditions--linear best replies and midpoint indifference--that pin down the classic linear-quadratic utility.

econ.TH↗

arXiv2024

Stable Matching as Transport: a Welfarist Perspective on Market Design

This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter indexes a planner's attitude towards inequality. This link offers insights into structural properties of matchings and trade-offs between objectives, showing how stability can lead to welfare inequalities, even among similar agents. Our model captures supply-demand imbalances in contexts like spatial markets, school choice, and ride-sharing. We also show that large markets with idiosyncratic preferences can be well approximated by aligned preferences, expanding the applicability of our results.

econ.TH↗

arXiv2023

Local Priority Mechanisms

We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every infeasible allocation. The mechanism then greedily attempts to match agents with their top choices. Whenever it reaches an infeasible allocation, the local compromisers move to their next favorite alternative. Local priority mechanisms exist for any constraint, so this provides a method of constructing new designs for any constrained allocation problem. We give axioms which characterize local priority mechanisms. Since constrained allocation includes many canonical problems as special constraints, we apply this characterization to show that several well-known mechanisms, including deferred acceptance for school choice, top trading cycles for house allocation, and serial dictatorship can be understood as instances of local priority mechanisms. Other mechanisms, including the Boston mechanism, are not local priority mechanisms. We give sufficient conditions for a local priority mechanism to be group strategy-proof. We also provide conditions which enable welfare comparisons across local priority mechanisms.

econ.TH↗

arXiv2023

A Topological Proof of The Gibbard-Satterthwaite Theorem

We give a new proof of the Gibbard-Satterthwaite Theorem. We construct two topological spaces: one for the space of preference profiles and another for the space of outcomes. We show that social choice functions induce continuous mappings between the two spaces. By studying the properties of this mapping, we prove the theorem.

econ.TH↗

arXiv2023

Royal Processions: Incentives, Efficiency and Fairness in Two-sided Matching

We study the set of incentive compatible and efficient two-sided matching mechanisms. We classify all such mechanisms under an additional assumption -- "gender-neutrality" -- which guarantees that the two sides be treated symmetrically. All group strategy-proof, efficient and gender-neutral mechanisms are recursive and the outcome is decided in a sequence of rounds. In each round, two agents are selected, one from each side. These agents are either "matched-by-default" or "unmatched-by-default." In the former case either of the selected agents can unilaterally force the other to match with them while in the latter case they may only match together if both agree. In either case, if this pair of agents is not matched together, each gets their top choice among the set of remaining agents. As an important step in the characterization, we first show that in one-sided matching all group strategy-proof and efficient mechanisms are sequential dictatorships. An immediate corollary is that there are no individually rational, group strategy-proof and efficient one-sided matching mechanisms.

econ.TH↗

arXiv2022

Efficiency in Random Resource Allocation and Social Choice

We study efficiency in general collective choice problems where agents have ordinal preferences and randomization is allowed. We explore the structure of preference profiles where ex-ante and ex-post efficiency coincide, offer a unifying perspective on the known results, and give several new characterizations. The results have implications for well-studied mechanisms including random serial dictatorship and a number of specific environments, including the dichotomous, single-peaked, and social choice domains.

econ.TH↗

arXiv2020

Incentives and Efficiency in Constrained Allocation Mechanisms

We study private-good allocation under general constraints. Several prominent examples are special cases, including house allocation, roommate matching, social choice, and multiple assignment. Every individually strategy-proof and Pareto efficient two-agent mechanism is a "local dictatorship." Every group strategy-proof N-agent mechanism has two-agent marginal mechanisms that are local dictatorships. These results yield new characterizations and unifying insights for known characterizations. We find all group strategy-proof and Pareto efficient mechanisms for the roommates problem. We give a related result for multiple assignment. We prove the Gibbard-Satterthwaite Theorem and give a partial converse. We also apply our characterization to task allocation and network regulation problems.

econ.TH↗