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Say that $c=2$, $\mathrm{\Delta}=1$, ${v}_{i}=100$, $b({v}_{i})=100$, and the agent’s beliefs about ${p}_{t-1}$ are such that ${h}_{i,t}\left(90\right)=0.3$ and ${h}_{i,t}\left(110\right)=0.7$. Then, ${q}_{i,t}\left(89\right)=1$ and ${q}_{i,t}\left(109\right)=0$ such that $\left({\mathrm{\pi}}_{i}|{H}_{i,t}\left({p}_{t-1}\right)\right)=0.3(100-89)-2=1.3$. Agent $i$ thus signals his willingness to observe the price. If given this opportunity, he will then buy the item if ${p}_{t}=89$ and not buy it if ${p}_{t}=109$.