Strategyproof matching with regional minimum and maximum quotas

This paper considers matching problems with individual/regional minimum/maximum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategyproof mechanisms that take such quotas into account. We first show that without any restrictions on the regional structure, checking the existence of a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (i.e., a tree), we show that checking the existence of a feasible matching can be done in time linear in the number of regions. We develop two strategyproof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Priority List based Deferred Acceptance with Regional minimum and maximum Quotas (PLDA-RQ) and Round-robin Selection Deferred Acceptance with Regional minimum and maximum Quotas (RSDA-RQ). When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible. We show that both mechanisms are fair. As a result, they are inevitably wasteful. We show that the two mechanisms satisfy different versions of nonwastefulness respectively; each is weaker than the original nonwastefulness. Moreover, we compare our mechanisms with an artificial cap mechanism via simulation experiments, which illustrate that they have a clear advantage in terms of nonwastefulness and student welfare

The Institutions of Federalism: Toward an Analytical Framework

Mature federations have relatively transparent delineations of authority among levels of government; subnational governments enjoy considerable autonomy in their expenditure, revenue, and debt policies. In other countries, problems of soft budget constraints, bailouts, and fiscal and financial instability demonstrate the difficulties of institutional design in a federation. This paper outlines an analytical framework within which interjurisdictional spillovers may create incentives for higher-level governments to intervene in the control and financing of lower-level governments (bailouts). This framework helps to identify directions for theoretical and empirical research that can illuminate important features of observed institutions and guide policy analysis.federalism, bailouts, soft budget constraint, externalities