Controlled choice over public schools attempts giving options to parents while maintaining diversity, often enforced by setting feasibility constraints with hard upper and lower bounds for each student type. We demonstrate that there might not exist assignments that satisfy standard fairness and non-wastefulness properties; whereas constrained non-wasteful assignments which are fair for same type students always exist.We introduce a "controlled" version of the deferred acceptance algorithm with an improvement stage (CDAAI) that finds a Pareto optimal assignment among such assignments. To achieve fair (across all types) and non-wasteful assignments, we propose the control constraints to be interpreted as soft bounds-flexible limits that regulate school priorities. In this setting, a modified version of the deferred acceptance algorithm (DAASB) finds an assignment that is Pareto optimal among fair assignments while eliciting true preferences. CDAAI and DAASB provide two alternative practical solutions depending on the interpretation of the control constraints.JEL C78, D61, D78, I20. * An earlier version (Ehlers, 2010) of this paper emerged from a joint project of the first author with Atila Abdulkadiroglu. We are grateful for his extensive comments and contribution to that paper. Ehlers acknowledges financial support from the SSHRC (Canada).

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The prevalent affirmative action policy in school choice limits the number of admitted majority students to give minority students higher chances to attend their desired schools. There have been numerous efforts to reconcile affirmative action policies with celebrated matching mechanisms such as the deferred acceptance and top trading cycles algorithms. Nevertheless, it is theoretically shown that under these algorithms, the policy based on majority quotas may be detrimental to minorities. Using simulations, we find that this is a more common phenomenon rather than a peculiarity. To circumvent the inefficiency caused by majority quotas, we offer a different interpretation of the affirmative action policies based on minority reserves. With minority reserves, schools give higher priority to minority students up to the point that the minorities fill the reserves. We compare the welfare effects of these policies. The deferred acceptance algorithm with minority reserves Pareto dominates the one with majority quotas. Our simulations, which allow for correlations between student preferences and school priorities, indicate that minorities are, on average, better off with minority reserves while adverse effects on majorities are mitigated. Terms of use: Documents in

A natural extension of superadditivity is not su¢ cient to imply that the grand coalition is e¢ cient when externalities are present. We provide a condition, analogous to convexity, that is su¢ cient for the grand coalition to be e¢ cient and show that this also implies that the (appropriately de…ned) core is nonempty. Moreover, we propose a mechanism which implements the most ef…cient partition for all coalition formation games and characterize the resulting payo¤ division.JEL Classi…cation Numbers: C71, C72, D62

In a first-price auction, asymmetries among bidders typically result in inefficient allocationsthat is, the winner of the auction may not be the person who values the object the most. This inefficiency creates a motive for post-auction resale, and when bidders take resale possibilities into account, their bidding behavior is affected as well. Standard models of such auctions, by and large, implicitly assume either that resale possibilities do not exist or that bidders do not take these into account when formulating bids.There are at least two reasons why resale possibilities should be considered explicitly. The first one is positive. If, after the auction is over, bidders see that there are potential gains from trade, then they will naturally engage in such trade. And it seems unlikely that the seller can prevent bidders from engaging in post-auction trade, even if, for some reason, resale was deemed disadvantageous. In the auction of spectrum licenses in the United Kingdom in 2000, post-auction trade was restricted by the government. The bidders, however, were easily able to circumvent these restrictions. TIW, a Canadian firm, bid successfully for the most valuable license "A" with a winning bid in excess of £4 billion. Hutchison, a telecommunications company, then acquired the license by buying TIW itself.Similarly, after the auction, France Telecom, an unsuccessful bidder, acquired Orange, a successful bidder. British Telecom created a wholly owned subsidiary that bid successfully in the auction. After the auction, this subsidiary was floated on the stock market and sold. Thus, restrictions on the buying and selling of licenses were circumvented by the buying and selling of companies that owned the licenses. The actions of Hutchison and British Telecom prior to the auction suggest that bidders fully anticipated post-auction resale possibilities.Actually, Hutchison had acquired a small stake in TIW prior to the auction and, in fact, provided funds for its bid. We are grateful to Kenneth Binmore and Tilman Börgers for providing us with details of the UK spectrum auctions. Asymmetric Auctions with Resale