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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.

Model

Strategic game:

  • players: bidders

  • 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?

36

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