Eyal Winter Center for the Study of Rationality The Hebrew University of Jerusalem

Herodotus of Ancient Greece 500 BC Women are sold for marriage by their families through auctions (they used Dutch Auctions). Auctions are held as mandatory for selling women into marriage.

Rome 193 AD Pertinax the Emperor is executed for the failing economy in Rome. The entire empire is sold by an auction to the highest bidder. Julianus wins the auction and becomes the new emperor.

Auction vs. Bargaining Auction: When the number of potential buyers is large and the seller’s information about the buyers’ willingness to pay is limited. Bargaining: Mainly in bilateral transactions or when the good has better-defined market value. In many cases one can combine an auction with bargaining (there are downsides and upsides).

Auction Types Common Value: All bidders have the same monetary value for the object but this value is unknown. Private Value: Different bidders have different values for the object but each bidder is fully informed about his own value (and is not informed about other bidders’ values).

The Winner’s Curse

Popular Auction Mechanisms First Price Sealed Bid: Bidders submit bids in sealed envelopes. The highest bidder wins the object and pays his bid. Second Price Sealed Bid: Like the first price sealed bid, except that the winner pays the second highest price instead of his own price. English Auction: The auction involves ascending prices. Bids are announced publicly and have to exceed those currently in the system. The winner is the last to bid.

Dutch Auction: A pointer points and there is a very high price that gradually declines. The pointer stops with the first “stop” call of a bidder. This bidder pays the price at which the pointer stops. Japanese Auction: The auction starts at a very low price that gradually rises. People leave the room when the price exceeds their willingness to pay. The last to remain wins and pays the price at which the next to last left the room.

Israeli Auction: Like first price sealed bid, except that the winner is the cousin of the mayor and he pays 50% of the lowest bid.

Vickery Theorem In the Second Price Sealed Bid auction, there is a dominant strategy for each bidder, which is to bid the true value of the object. Proof: Denote by x the highest bid (apart from mine). Assume that my value for the object is 1000 EUR. If x < 1000, then any bid above x will make me the winner and will make me pay x. Any bid below x will make me lose. So saying 1000 is best.

If x > 1000, then bidding above x will make me win the object but lose money, and bidding below x (regardless of the bid and including 1000) will give me zero profit. Proxy servers in Internet auctions create a second price mechanism.

The Equivalence of Auction Mechanisms First Price Sealed Bids and Dutch Auctions are equivalent. Second Price Sealed Bids and English Auctions are equivalent. The Revenue Equivalence Theorem (Vickery 1961; Myerson 1980): All efficient auctions are revenue equivalent.

The Analysis of First Price Auctions v 1,…v n (bidders’ valuations) are iid with the cumulative distribution F. b(v) is the bidding function of each player. In equilibrium each player’s bidding function has to maximize his expected profit, given the bidding functions of the rest. Expected profit of player i is given by E i (b)= P (player i has the highest bid) [v – b(v)].

P(i’s the highest bid) = P(b i (v i )) > b j (v j )) for all j ≠i) = p(v i > v j for all j ≠i) = [F(v i )] n-1 E(b)= [F(v i )] n-1 [v-b(v)] Equilibrium Conditions: argmax w [F(w)] n-1 [v-b(w)]=v (n-1)[F(w)] n-2 F’(w)[v-b(w)]-b’(w)[F(w)] n-1 | w=vi = 0 (n-1)F’(v)[v-b(v)]=b’(v)[F(v)]

Solution If v i ~ U[0,1] then b(v) =

Laboratory Results First price auctions generate more revenue than Dutch auctions. Average bids increase with the number of bidders in the auction.

The Cellular Auctions From 1993 to 2001 governments in the world made a revenue of 100 billion USD. In 1994 the New York Times announced the British Cellular Auction as the largest auction ever, totaling a revenue of 34 billion USD. Ken Binmore designed the auction and became Sir Ken Binmore.

The New Zealand Failure The auction used was second price sealed bids. On one batch of frequencies the highest bid was 7 million NZD, and the second highest bid only 5000 NZD. On another batch the highest bid was 100,000 and the second highest only 6 NZD!!!

The FCC Auction in the US The auction runs in stages. At each stage each bidder can introduce new bids and withdraw his existing bids. New bids have to exceed those in the system. Bids that are withdrawn incur a potential fine on the bidder. The bidder has to pay the difference between his withdrawn bid and the price at which the batch is eventually sold.

Auctions in Google Any query in Google earns around 10 cents for the company! The participating companies compete on the location in the ad and bid on any query. Google estimates the number of clicks per query for each company and ranks pages to maximize revenue.

Large Auctions in Israel In 2006 the government share in the national telephone company was sold in an auction. The highest bid was around 200m EUR. After the auction ended the government requested an additional 6m EUR and received it. Is it a good strategy?

The country’s storage facilities for gas were sold in There were 3 sites. The mechanism used was a combinatorial auction (with ascending prices). The government earned 350m EUR where expert estimates were about 60m EUR. The largest Israeli newspaper announced this auction as the most successful one in the history of the country.

Legal Issues in Auctions Collusion: Why is it banned by most governments? Around 50% of the Anti-Trust cases in the US are on collusion in auctions.

Other “Tricks” Sellers “hide” reservation prices and make bidders believe that they will sell to the highest bidder at any price. Sellers make fictitious bids to boost prices in auctions. They inform one bidder of the price of another bidder to get a higher price.

Why is it wrong to allow it? Manipulation destroys the efficiency of the market mechanism.

“Tacit” Collusion in Auctions On batch no. 128 in the US FCC auction someone bids 1,000,129! The California Electricity Market: Tacit collusion requires long term interactions between bidders. Contracts in the electricity market in CA were too short and facilitated long-term interactions (Repeated Games).

Behavioral Aspects of Auctions Snipping The Afternoon Effect