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We study the problem of centralized allocation of children to public day care centers, illustrated by the case of Denmark. Our framework applies to problems of dynamic matching in which there is entry and exit of agents over time; for example, the school choice problem once student mobility is taken into account. We show that there does not exist any mechanism that is both stable and strategy-proof. We also show that the well-known Top Trading Cycles mechanism is neither Pareto efficient nor strategy-proof. Finally, a mechanism in which parents sequentially choose menus of schools is both strategy-proof and Pareto efficient. (JEL C73, D82, I21)

We study the implementation of constrained-efficient allocations in labour markets where a basic coordination problem leads to an equilibrium matching friction. We argue that these allocations can be achieved in a non-cooperative equilibrium if wages are determined by ex post bidding. This holds true even in finite-sized markets where the equilibrium-matching process has decreasing returns to scale -where the 'Hosios rule' does not apply -both with and without heterogeneity. JEL classification: D83, J64Enche`re ex post et choˆmage efficient de coordination. Les auteurs e´tudient la mise en oeuvre d'allocations axe´es sur l'efficacite´dans des marche´s du travail ou`un proble`me fondamental de coordination engendre un e´quilibre frictionnel. On sugge`re qu'on peut atteindre ces allocations dans un e´quilibre sans coope´ration si les niveaux de salaires sont de´termine´s par des enche`res ex post. Cela demeure vrai meˆme dans des marche´s de taille finie ou`le processus d'e´quilibration fait l'expe´rience de rendements de´croissants a`l'e´chelle -la`ou`la re`gle d'Hosios ne s'applique pas -a`la fois quand il y a et qu'il n'y a pas d'he´te´roge´neite´.

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We compare equilibrium allocations in directed search models where prices are determined alternatively by posting and by competing auctions, with the following results. With finite numbers of players, sellers' expected payoffs are higher when all sellers auction than when all sellers post. This difference is largest in the 2-by-2 case, where payoffs to sellers are 1/3 higher if they auction. The difference in the payoffs decreases rapidly with market size and vanishes in the limit "large" economy. When sellers can choose whether to post prices or auction in the 2-by-2-case, all combinations (auction-auction, post-post, and auction-post) can occur in equilibrium if sellers choose mechanism and price simultaneously. However, if sellers choose mechanism before price then the dominant strategy equilibrium has both sellers auctioning.