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We provide necessary and sufficient conditions on the preferences of market participants for a unique stable matching in models of two-sided matching with non-transferable utility. We use the process of iterated deletion of unattractive alternatives (IDUA), a formalisation of the reduction procedure in Balinski and Ratier (1997), and we show that an instance of the matching problem possesses a unique stable matching if and only if IDUA collapses each participant preference list to a singleton. (This is in a sense the matching problem analog of a strategic game being dominance solvable.)
In a many-to-one matching model in which firms preferences satisfy substitutability, we study the set of worker-quasi-stable matchings. Worker-quasi-stability is a relaxation of stability that allows blocking pairs involving a firm and an unemployed
We highlight the tension between stability and equality in non transferable utility matching. We consider many to one matchings and refer to the two sides of the market as students and schools. The latter have aligned preferences, which in this conte
We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose--accept rounds executed by the Gale--Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost s
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students preferences are monotone in contract terms. We show that equivalence, properly defined, to a choice profile
We study the three-dimensional stable matching problem with cyclic preferences. This model involves three types of agents, with an equal number of agents of each type. The types form a cyclic order such that each agent has a complete preference list