12

Say that $c=2$, $\mathrm{\Delta }=1$, ${v}_{i}=100$, $b\left({v}_{i}\right)=100$, 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 $\left({\mathrm{\pi }}_{i}|{H}_{i,t}\left({p}_{t-1}\right)\right)=0.3\left(100-89\right)-2=1.3$. 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 ${p}_{t}=109$.