Duygu Sili

Italian public schools are legally granted autonomy in allocating students across classrooms, but competitive pressure from demographic decline renders this autonomy largely illusory. In under-demanded catchment areas, competition leads schools to sort students by economic and sociocultural status (ESCS) as a dominant strategy resembling a prisoner's dilemma. Using INVALSI data for elementary and middle schools, we compute municipality-averaged within-school segregation indices (dissimilarity and distance) based on ESCS and show that a larger five-year decline in the school-entrant population causes more within-school segregation; the result is robust to random- and fixed-effects specifications and to instrumental-variable estimation.

We study a stylized model of a future logistics market in which an independent market operator assigns last-mile parcel deliveries to competing service providers. Customers value providers through attributes such as environmental performance and service quality, while each provider's per-parcel tariff decreases with the number of customers it serves, reflecting routing economies of scale. An assignment is self-enforcing if no customer would rather switch provider at the tariff she would actually pay after switching; the resulting game is a resource-selection game with an exact potential, so self-enforcing assignments (pure Nash equilibria) always exist and every maximal sequence of profitable unilateral switches reaches one. Scale economies, however, make equilibria multiple and very different: a market can be locked into a provider that nobody prefers. With two providers we characterize the equilibrium set completely and show that the operator reaches the payment-minimizing equilibrium by choosing the order in which providers are activated; with three or more providers no activation order is reliable in general, so we optimize any operator objective over the equilibrium set with a mixed-integer program and a clustering-based reduction that scales beyond 2,500 customers. In a study calibrated to parcel demand in a district of Istanbul, the utility gap between the best and worst equilibria ranges from 7% to 18% (median 16%), and the utility-maximizing equilibrium always lies on the environmental–quality efficient frontier.

We develop a new methodology that characterizes and computes dynamically optimal mechanisms for bilateral matching over arbitrary state spaces, provided that compatibility between agent types follows a linear spatial structure. The optimal value function is shown to be D-multimodular, and the resulting second-order properties—componentwise concavity, superconcavity, and sub- and supermodularity—extend recent advances in Markov decision processes and queueing systems, which focus on substitutable components, to environments with complementarities. Applied to kidney exchange, the framework relaxes the assumption that overdemanded pairs are matched on arrival and shows that a multi-threshold, possibly anti-greedy, mechanism is optimal.

Schools that assign students to classrooms of fixed size increasingly impose diversity quotas to prevent within-school segregation, while students and their parents have preferences over classmates and lobby for reassignments. We ask when a quota-compliant assignment is stable against coalitions of students who reorganise across classrooms within capacities and quotas, and what fairness costs in welfare and in stability. Coalitional moves divide into exchanges, whose members do not form new ties with one another, and mergers. Along an exchange the coalition's gains are mirrored by the students left behind, welfare is a potential, and the welfare-optimal fair assignment cannot be blocked by any exchange; along a merger welfare can fall, adjustment can cycle, and the welfare optimum can be blocked. Whether the conflict can destroy stability altogether is decided by classroom capacities alone: with at most two classrooms of size above one, or with all active classrooms of size two, a stable fair assignment exists for every quota system, whereas otherwise classroom-specific composition targets can leave every fair assignment blocked. We separate the price of fairness from the price of stability, show that a common own-type premium moves the welfare optimum towards segregation while exact common targets neutralise it, that welfare maximisation can be manipulated by withholding friendships, and that one-sided friendships can empty the core even with two classrooms.

We study the assignment of a cohort of students carrying an exogenous protected attribute to k classrooms of prescribed sizes, when students have additively separable preferences over classmates and every classroom is required to be balanced: its group counts must equal the largest-remainder (Hamilton) apportionment of the population shares. The balanced set is parameter-free, non-empty, and closed under same-type cyclic exchanges. We propose a two-phase mechanism—proportional initialisation followed by a cycle-refinement dynamics—and show that it terminates at a balanced cycle-stable partition: a balanced partition that no coalition of students in distinct classes can leave, by rotating along a cycle of classes, while remaining balanced and making every member strictly better off. Existence is constructive, the dynamics is governed by the within-class affinity potential, the constrained welfare optimum is itself cycle-stable, and the set of balanced cycle-stable partitions is the unique von Neumann–Morgenstern stable set of the balanced set under the dominance relation generated by chains of improving cyclic deviations. We quantify path-dependence, characterise exactly when randomised restarts recover the constrained welfare optimum, extend the framework to several protected attributes through a lexicographic balance criterion, and report simulation evidence.