First-price sealed-bid auction

A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids, so that no bidder knows the bid of any other participant. The highest bidder pays the price they submitted.

In a FPSBA, each bidder is characterized by his/her monetary valuation of the item for sale.

Suppose Alice is a bidder and her valuation is a. Then, if Alice is rational:

Alice would like to bid the smallest amount that can make her win the item, as long as this amount is less than a. For example, if there is another bidder Bob and he bids ${\displaystyle y}$ and ${\displaystyle y<a}$, then Alice would like to bid ${\displaystyle y+\varepsilon }$ (where ${\displaystyle \varepsilon }$ is the smallest amount that can be added, e.g. one cent).

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