Efficient Auctions Flashcards
What is the revelation principle?
It states that for any outcome achievable through some mechanism (with or without truth-telling), there is an equivalent mechanism in which all participants truthfully reveal their private information (such as preferences, valuations, or types). Truth telling is then an equilibrium in dominant strategies that induces the utilitarian outcome
What are auctions?
Auctions are particular mechanisms that map bids to an allocation (who gets the good), and payments (who pays what). It serves as a mechanism for price discovery.
What are the characteristics of a First Price Auction ?
The bidders submit sealed bids.
The seller opens the bids.
The bidder who submitted the highest bid wins the auction.
The winner pays his own bid.
What should you bid in an FPA?
It is best to bid slightly below your value, so that b-v is positive, and you make a gain, so even if you’re less likely to win, at least you can make a profit. However, there is no dominant strategy.
Why is there no dominant strategy in an FPA?
Because you can make an improvement, so be better off either placing a lower, or a higher bid (which are two
different strategies). It may depend on other bids.
What is an Ascending Auction ?
It is an auction where price starts at zero and rises slowly :
* Buyers indicate their willingness to continue bidding (e.g. keep their
hands up) or can exit.
* The auction ends when just one bidder remains.
* The remaining bidder wins and pays the price at which the second remaining bidder dropped out.
How should you bid in an Ascending Auction?
An optimal, weakly dominant strategy is to continue bidding until the price just equals your value.
What is a Second Price Auction?
It is an auction where bidders submit sealed bids that are opened later, and when they are revealed, the bidder who submitted the highest bid wins the auction, but they pay the second-highest bid.
What is the difference between the SPA and the Ascending Auction?
The bidding process is different : private and simultaneous vs public and iterative
How should you bid in an SPA?
Theorem : it is a (weakly) dominant strategy to bid your value in a second price auction.
What is the equilibrium in an SPA?
Everyone bids their value, the bidder with the highest bid wins the auction (same outcome as the ascending auction)
What is the equilibrium in an FPA?
It is a symmetric Nash equilibrium under the canonical model. Since the bidders don’t want to bid their true value in an FPA, they choose to have strategies (bidding functions). In consequence, in a symmetric Nash equilibrium, all bidders use the same bidding function as best responses to each other.
On what does the choice of a bid depend in an FPA?
The optimal bid depends on what you think the others will do (unlike the second price auction).
What is the symmetric Nash equilibrium in an FPA with two players with values distributed on [0,1]?
vi/2. In this case, we can recover the true value from the bid : vi=2bi
How can you formulate an expected payoff in an FPA?
Payoff = (vi − bi) x Probability of winning
