How to (Carefully) Breach a Service Contract?

Consider a firm $$\mathcal {S}$$ providing support to clients $$\mathcal {A}$$ and $$\mathcal {B}$$. The contract $$\mathcal {S} \leftrightarrow \mathcal {A}$$ stipulates that $$\mathcal {S}$$ must continuously serve $$\mathcal {A}$$ and answer its calls immediately. While servicing $$\mathcal {A}$$, $$\mathcal {S}$$ incurs two costs: personnel fees salaries that $$\mathcal {A}$$ refunds on a per-call-time basis and technical fees that are not refunded. The contract $$\mathcal {S} \leftrightarrow \mathcal {B}$$ is a pay-per-call agreement where $$\mathcal {S}$$ gets paid an amount proportional to $$\mathcal {B}$$'s incoming call's duration. We consider that the flow of incoming $$\mathcal {B}$$ calls is unlimited and regular. $$\mathcal {S}$$ wishes to use his workforce for both tasks, switching from $$\mathcal {A}$$ to $$\mathcal {B}$$ if necessary. As $$\mathcal {S} \leftrightarrow \mathcal {B}$$ generates new benefits and $$\mathcal {S} \leftrightarrow \mathcal {A}$$ is the fulfilling of a contracted obligation, $$\mathcal {S}$$ would like to devote as little resources as necessary to support $$\mathcal {A}$$ and divert as much workforce as possible to serve $$\mathcal {B}$$. Hence, $$\mathcal {S}$$'s goal is to minimize his availability to serve $$\mathcal {A}$$ without incurring too high penalties. This paper models $$\mathcal {A}$$ as a naive player. This captures $$\mathcal {A}$$'s needs but not $$\mathcal {A}$$'s game-theoretic interests --- which thorough investigation remains an open question.