Chapter 4 provides the theoretical framework for suspects’ invocations for counsel in the book’s corpus. The analysis will focus on the discursive features of suspects’ invocations for counsel during custodial interrogation, as well as the sequences of talk that follow the suspects’ invocations. This part of the analysis will use applied game theory, specifically hypergame theory, to describe police-suspect exchanges after a suspect invokes counsel. The model of the invocation game of police interrogation extends signal analysis from simple signaling games into extended conversations based on strategic objectives. This application of game theory to the invocation stage of an interrogation shows how an interrogator can manipulate a custodial suspect to change their preference to invoke counsel due to the ambiguities created by case law, which designates interrogators as arbiters of what constitutes an unequivocal invocation of the right to counsel, and stylized by formal training that encourages interrogators to engage in strategic discourse with suspects to maintain the possibility of obtaining statements.