First-price auction Another auction form:
auctioneer begins by announcing a high price
price is gradually lowerered until someone indicates a
willingness to buy the object at that price.
actions of each player: set of possible bids (nonnegative numbers)
preferences of player i: represented by a payoff function that gives player i vi − p if she wins (where vi is her valuation and p is her bid) and 0 otherwise.
This is a first-price sealed-bid auction.
One Nash equilibrium
(v2, v2, v3, . . . , vn) Outcome: player 1 obtains the object at the price v2. Why is this a Nash equilibrium?