\begin{definition}[Definition:Sealed-Bid Auction]
A '''sealed-bid auction''' is a game in the following format:
An object $F$ is to be assigned to a player in a set $\left\{ {1, 2, \ldots, n}\right\}$ in exchange for a payment.
The valuation of $F$ by player $i$ is $v_i$, and:
:$v_1 > v_2 > \cdots > v_n > 0$
Each player simultaneously submits a non-negative number, called a '''bid'''.
$F$ is then given to the player with the lowest index among those who submit the highest bid, in exchange for a payment.
\end{definition}