Abstract
Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced.
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Romero-Medina, A., Triossi, M. Games with capacity manipulation: incentives and Nash equilibria. Soc Choice Welf 41, 701–720 (2013). https://doi.org/10.1007/s00355-012-0703-1
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DOI: https://doi.org/10.1007/s00355-012-0703-1