 Posted price

A posted price is a fixed price announced by a seller, who sells if an eligible buyer accepts. Suppose two buyers have independent values with common cumulative distribution function $F$, and a buyer accepts exactly when its value is at least the price $p\ge 0$. The no-sale probability is $F(p-{)}^2$, where $F(p-)=\mathrm{Pr}(V<p)$, so expected seller revenue isFor a continuous value distribution this becomes $p(1-F(p{)}^2)$. With an atom at $p$, using $F(p)$ instead would exclude buyers who are indifferent and agree to buy. A convention that indifferent buyers decline has that strict-acceptance formula instead. Selecting among several accepting buyers does not affect revenue when each pays the same posted price.