Child Care Allocation Mechanisms: Navigating Incomplete Preference Elicitation

Child care allocation markets in Germany widely employ variants of the Gale-Shapley Deferred Acceptance (DA) mechanism (Gale & Shapley, 1962) to match children to child care centers. However, implementers often make seemingly minor adjustments to the original mechanism without thoroughly evaluating their implications. We show that these adjustments can significantly affect a mechanism's desirable properties. Adjustments are necessary on these markets as care durations, capturing the contractual terms agreed upon by children and child care centers, are key to finding an allocation. Thus, we model a child care allocation problem with care durations. We demonstrate how the cumulative offer process, as developed for matching with contracts (Hatfield & Milgrom, 2005), can be effectively adapted to our context. However, a key practical disadvantage is that this mechanism requires full preference disclosure from participants, which is often unrealizable in real-world settings. We analyze how existing practical implementations of the DA deal with incomplete preference elicitation and examine the implications of these approaches. Our comparative analysis reveals that one mechanism from practice offers a distinct advantage over the others when considering incomplete preference elicitation.