Lampson's confinement problem asks how to prevent a program that processes confidential information from leaking it to a third party. We introduce the strategic confinement problem, which arises when the communicating parties are strategic agents with shared coordination resources. In this setting, residual communication capacity can be concentrated on low-entropy, high-impact predicates of the confidential data. Consequently, bounds on information leakage need not induce corresponding bounds on worst-case harm: a channel with negligible capacity may still suffice to select damaging outcomes. We argue that systems of learnt strategic agents naturally instantiate this problem because they do not admit complete behavioural specifications, their learnt conventions generally cannot be predicted or reproduced by an external observer, and sufficiently capable agents can construct covert communication schemes that are difficult to detect or eliminate. Our contribution is therefore not a new theory of communication, but a reinterpretation of confinement in the presence of strategic agents. Classical confinement bounds what information may flow; strategic confinement highlights that this need not bound what strategic agents can jointly achieve.