Transparent matching mechanisms - Markus Möller (University of Bonn and University of Cologne, Reinhard Selten Institute (RSI), 2024)
I study a central authority's ability to commit to a publicly announced mechanism in a one-to-one agent-object matching model. The authority announces a strategy-proof mechanism and then privately selects a mechanism to initiate a matching. An agent's observation in form of the final matching has an innocent explanation (Akbarpour and Li, 2020), if given the agent's reported preferences, there is a combination with other agents' preferences leading to an identical observation under the announced mechanism. The authority can only commit up to safe deviations (Akbarpour and Li, 2020)-mechanisms that produce only observations with innocent explanations. For efficient or stable announcements, I show that no safe deviation exists if and only if the announced mechanism is dictatorial. I establish that the Deferred Acceptance (DA) Mechanism (Gale and Shapley, 1962) implies commitment to stability. Finally, I show that group strategy-proof and efficient announcements allow commitment to efficiency only if they are dictatorial.
Keywords: C78; D47; D82; 330; Matching; Transparency; Partial Commitment; Strategy-Proof; Stability; Efficiency; DA; TTC