Continuum behaviors are discussed in some detail by Schelling, and interestingly they can be used by both parties. Here they make the blackmail more effective. If the payment is lump-sum, the blackmailer can't be trusted, and so the movie start won't pay. The continuous payment option gives her a way to pay the blackmailer and expect him to stay quiet, which makes her more vulnerable to blackmail in the first place.

Continuous options can also be used to derail threats, when the person being threatened can act incrementally and there is no bright line to force the action (assuming the threat is to carry out a single action).