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2011 Documento de Trabajo #280

Games with Capacity Manipulation: Incentives and Nash Equilibria

Studying the interaction between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and su!cient 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 capacity manipulations games where 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.

JEL Classification Numbers: C71, C78, D71, D78.

Antonio Romero-Medina
Matteo Triossi

Keywords: Capacity, Cycles, Nash equilibrium, Stable matching