Belykh, Andrei (2025) Three Essays on Matching theory. [Tesi di dottorato]

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Abstract

This dissertation investigates how collective allocation and coalition-formation mechanisms perform when individual preferences exhibit interdependencies, and when classical notions of stability become unattainable or insufficient. The first chapter studies school choice in environments with peer-dependent preferences, where each student’s utility depends not only on the assigned school but also on the composition of peers. Such externalities eliminate the possibility of stable assignments. Nevertheless, the Rank-Minimizing mechanism retains its Non-Obvious Manipulability property in this richer environment, which is the main result of the first chapter. The second chapter examines the weak strategic properties of school choice mechanisms more broadly. It shows that, for unanimous mechanisms, regret-free truth-telling implies non-obvious manipulability, but not vice versa. The RM-SD mechanism serves as a concrete example in which non-obvious manipulability holds without guaranteeing regret-free truthful reporting. Taken together, these results establish a more complete hierarchy of strategic properties, ranging from obvious strategy-proofness to mechanisms that are clearly manipulable. The third chapter turns to decentralized insurance markets and analyzes the endogenous formation of reinsurance pools as a hedonic coalition game. Insurers differ in capital endowments and probabilities of bankruptcy, and a solvency regulation parameter limits the aggregate risk exposure of any coalition. Under mild homogeneity of risk characteristics and strictly monotone preferences for more reliable partners, the induced game admits a unique core-stable partition: the stable coalitions consist of consecutive sets of the most reliable firms. This result characterizes how capital regulation shapes coalition structure and identifies the endogenous organization of risk-sharing arrangements. Taken together, the dissertation advances our understanding of matching and coalition-formation mechanisms in environments with externalities and strategic complexity. It highlights settings in which stable assignments or core outcomes fail to exist and classical incentive compatibility notions weaken, yet mechanisms can still deliver behaviorally robust and economically meaningful allocations.

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