Posted price (source code)

= Posted price
{title2=$p$}

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 $p\ge0$. The no-sale probability is $F(p-)^2$, where $F(p-)=\Pr(V<p)$, so <expected seller revenue> is
$$
p\bigl(1-F(p-)^2\bigr).
$$
For 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>.