Stable Matching with Mistaken Agents

Perceived Ability and School Choices: Experimental Evidence and Scale-Up Effects

“…While we estimate the school choice model (1) by assuming stable matching but not truth-telling, we can allow students to be truthful in order to study matching outcomes. This holds as long as preference estimates are consistent (Artemov et al 2023). We use the simulated rank-ordered 11 One potential caveat with our school choice framework is that it precludes applicants from reacting to (expected) policy-induced changes in peer composition across schools.…”

Identification and Estimation in Many‐to‐One Two‐Sided Matching Without Transfers

“…That is, no college prefers to reject any of its currently matched students to vacate a seat, and no student prefers to leave her current match to become unmatched or matched with a college that is willing to accept her and, if necessary, reject one of its currently matched students. Stability is often imposed in the study of various matching markets (see, for a survey, Chiappori and Salanié (2016)) and is satisfied in equilibrium in our setting in certain game‐theoretical models (Artemov, Che, and He (2023), Fack, Grenet, and He (2019)).…”

“…Our setting contains one single matching game that changes with the market size. Proposition 3 of Azevedo and Leshno (2016), Proposition 4 of Fack, Grenet, and He (2019), and Corollary 2 of Artemov, Che, and He (2023) imply that, under certain conditions, the equilibrium outcome in the continuum approximates well an equilibrium outcome in a large finite market. Such an approximation is also used in the network literature (e.g., Menzel (2022)).…”

“…99 Stability can be achieved in certain equilibrium if students apply to all acceptable colleges and if a stable mechanism, for example, the deferred acceptance (Gale and Shapley (1962)), is used to find the matching. Theoretically, provided that students know what criteria colleges use to rank them, stability can still be satisfied in equilibrium, even if students choose not to apply to all acceptable colleges due to application costs (Fack, Grenet, and He (2019)) or if students make certain application mistakes (Artemov, Che, and He (2023)). Importantly, achieving stability does not require the market to be centralized, as shown in laboratory experiments (see, e.g., Pais, Pintér, and Veszteg, 2020), and steps in mechanisms such as the deferred acceptance can be implemented in a decentralized fashion (Grenet, He, and Kübler (2022)). …”