arXiv subjects

Maxwell Allman

Publications and source records attributed to Maxwell Allman.

3 recordsLinked to original sources

arXiv2025

From signaling to interviews in random matching markets

In many two-sided labor markets, interviews are conducted before matches are formed. The growing number of interviews in medical residency markets has increased demand for signaling mechanisms, where applicants send a limited number of signals to communicate interest. We study the role of signaling mechanisms to reduce interviews in centralized random matching markets where initial preferences are refined through interviews. Agents can only match with those they interview. For the market to clear, we focus on perfect interim stability: no pair of agents-even if they never interviewed each other-prefers each other to their assigned partners under their interim preferences. A matching is almost interim stable if it is perfect interim stable after removing a vanishingly small fraction of agents. We analyze signaling mechanisms in random matching markets with $n$ agents where agents on the short side, long side, or both sides signal their top $d$ preferred partners. The interview graph connects pairs where at least one party signaled the other. We reveal a fundamental trade-off between almost and perfect interim stability. For almost interim stability, $d=\omega(1)$ signals suffice: short-side signaling is always effective, whereas long-side signaling is effective only when the market is weakly imbalanced, i.e., when any size difference between the two sides becomes negligible as the market grows. For perfect interim stability, at least $d=\Omega(\log^2 n)$ signals are necessary, and short-side signaling becomes crucial in any imbalanced market. We establish that truthful signaling is a Bayes-Nash equilibrium and extend our analysis to markets with hierarchical structure. As a technical contribution, we develop a message-passing algorithm that efficiently determines interim stability by leveraging local neighborhood structures.

cs.GT↗

arXiv2023

Interviewing Matching in Random Markets

In many centralized labor markets candidates interview with potential employers before matches are formed through a clearinghouse One prominent example is the market for medical residencies and fellowships, which in recent years has had a large increase in the number of interviews. There have been numerous efforts to reduce the cost of interviewing in these markets using a variety of signalling mechanisms, however, the theoretical properties of these mechanisms have not been systematically studied in models with rich preferences. In this paper we give theoretical guarantees for a variety of mechanisms, finding that these mechanisms must properly balance competition. We consider a random market in which agents' latent preferences are based on observed qualities, personal taste and (ex post) interview shocks and assume that following an interview mechanism a final stable match is generated with respect to preferences over interview partners. We study a novel many-to-many interview match mechanism to coordinate interviews and that with relatively few interviews, when suitably designed, the interview match yields desirable properties. We find that under the interview matching mechanism with a limit of $k$ interviews per candidate and per position, the fraction of positions that are unfilled vanishes quickly with $k$. Moreover the ex post efficiency grows rapidly with $k$, and reporting sincere pre-interview preferences to this mechanism is an $\epsilon$-Bayes Nash equilibrium. Finally, we compare the performance of the interview match to other signalling and coordination mechanisms from the literature.

econ.TH↗

arXiv2021

Complexity of Source-Sink Monotone 2-Parameter Min Cut

There are many applications of max flow with capacities that depend on one or more parameters. Many of these applications fall into the "Source-Sink Monotone" framework, a special case of Topkis's monotonic optimization framework, which implies that the parametric min cuts are nested. When there is a single parameter, this property implies that the number of distinct min cuts is linear in the number of nodes, which is quite useful for constructing algorithms to identify all possible min cuts. When there are multiple Source-Sink Monotone parameters and the vector of parameters are ordered in the usual vector sense, the resulting min cuts are still nested. However, the number of distinct min cuts was an open question. We show that even with only two parameters, the number of distinct min cuts can be exponential in the number of nodes.

cs.DM↗