Definition:Sealed-Bid Auction

Definition
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.