= Solution
The <instrumental variable> graph is
$$
Z\longrightarrow A\longrightarrow Y,
\qquad
U\longrightarrow A,
\qquad
U\longrightarrow Y,
$$
with no arrow $Z\to Y$ and no common cause of $Z$ with $A$ or $Y$.
In <potential outcome> notation, a valid instrument requires:
* <Instrumental-variable independence>: $Z\perp\{A(0),A(1),Y(0),Y(1)\}$, strengthened to all relevant joint potential outcomes as needed. Coin flipping makes the incentive assignment independent of quitting behavior and blood pressure under either assignment.
* <Exclusion restriction>: $Y(z,a)=Y(a)$. The incentive can affect blood pressure only by changing whether the subject quits, not through stress, income, or another direct route.
* <Instrument relevance>: $\mathbb P\{A(1)\ne A(0)\}>0$, or at least $\mathbb E[A(1)-A(0)]\ne0$. The monetary incentive must change quitting probability.
* <Consistency of potential outcomes> and no interference: observed quitting and blood pressure equal the potential values under the assigned encouragement and received exposure, and one subject's assignment does not affect another's outcome.
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