Many infrastructure systems are governed by non-monetary capacity allocation: users submit scheduling requests and an infrastructure manager determines a schedule of utilization given capacity restrictions. Two broad approaches exist to cope with information asymmetry. Under a primary mechanism, the infrastructure manager determines the eventual schedule. Under a secondary mechanism, users can swap their service units following the scheduling adjustments from the infrastructure manager. The secondary mechanism provides flexibility to align the schedule with users’ (private) preferences. However, this paper shows that the secondary mechanism may not result in more efficient outcomes when users are strategic. We develop a multi-stage capacity allocation game in infrastructure systems characterized by multi-period operations, discrete service units and non-atomistic users. We show that the primary mechanism either is incentive compatible, or incentivizes users to voluntarily displace low-value service units from peak to off-peak periods. Such “good gaming” behaviors mitigate system-wide costs. In contrast, the secondary mechanism incentivizes users to request more service units than preferred in peak periods. Such “bad gaming” behaviors increase system-wide costs. The costs from “bad gaming” may outweigh the benefits from secondary swaps: system-wide costs can be lower under the (restricted) primary mechanism than under the (flexible) secondary mechanism.