Matching with Waiting Times: The German Entry-Level Labour Market for Lawyers

We study the allocation of German lawyers to regional courts for legal trainee-ships. In a given period there are more applicants than available positions in some regions, thus not all lawyers can be matched simultaneously. Consequently, some lawyers must wait before they are allocated. We analyze the currently used "Berlin" mechanism and demonstrate that it is not weakly Pareto efficient, does not eliminate justified envy and does not respect improvements. We introduce a matching with contracts model, using waiting time as the contractual term. Despite the failure of the unilateral substitutes condition, under a weak assumption on lawyers' preferences, a lawyer-optimal stable allocation exists, given an appropriate choice function for the courts. Using existing results, we show that the resulting mechanism is strategy-proof, weakly Pareto efficient as well as eliminating justified envy and respecting improvements. Finally we extend our proposed mechanism to allow for a more flexible allocation of positions over time.