Mock Auction of Laguardia Arrival/Departure Slots The
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Why Auctions? Mock Auction of LaGuardia Efficiency Short run: resources to best use Arrival/Departure Slots Long run: correct incentives for investment Auctions are robust Lawrence M. Ausubel and Peter Cramton Auctions are responsive University of Maryland Auctions are flexible February 2005 Easily accommodate any division of revenues Auctions vs. High Density Rule Auctions vs. Congestion Pricing Both limit quantity to avoid excessive congestion Both seek efficient pricing Auction uses efficient pricing to maximize social Auctions provide stability of long-term slot leases and welfare predictable (low) congestion levels Congestion pricing gives airlines flexibility to quickly Auction revenues can replace distortionary fees and change schedules at expense of less predictability in taxes airport loads and delays Annual auctions allow entry and exit in dynamic industry Auctions vs. Congestion Pricing Congestion pricing: fix price; quantity determined by market Auction: fix quantity; price determined by market Absent uncertainty, two approaches are the same The Proposed Design Better approach depends on what is most uncertain Congestion pricing — if prices are known and quantities are uncertain Auction — if quantity is known and prices uncertain Here we know quantity (maximum throughput of LaGuardia), but we don’t know prices needed to achieve quantity Simultaneous Clock Auction Auction Design Simultaneous Easy to use All slots up for auction at the same time Web browser and spreadsheet Ascending clock Price discovery focuses bidder decision making on Auctioneer announces prices and bidders respond with relevant alternatives the quantity demanded at these prices Prices increase on slots with excess demand Activity rule protects against insincere bidding, Provides essential price discovery during the auction enhancing price discovery Auction ends when no excess demand Package bids Bids must be roughly consistent with profit maximization – Reduce demands as prices increase Allows bidders to buy what they want given the prices – Can’t shift quantity to slots that become relatively more expensive No risk that you will win just part of what you need Approach is well tested Single Product Clock Auction – 0900 Slot Spectrum auctions Price Round 6 Closing Price: P6 Electricity auctions Round 5 P5 Round 4 P4 Pollution permit auctions Round 3 P3 Experimental lab Round 2 P2 Round 1 P1 Slots Supply Aggregate Demand = 32 Many products: 0600, 0700, …, 2100 Auctioneer specifies price vector I: Single-Product Bidder responds with quantity vector Clock Auctions As prices increase, bidders can: Shift to less expensive hours Reduce quantity (upgauge or reduce service) Drop unprofitable markets Single Product Clock Auction – Aggregate Demand Single Product Clock Auction – Avoiding Overshoot Price Price Overshoot Round 6 Round 6 Closing Price: P6 Closing Price: P6 Round 5 Round 5 P5 P5 Round 4 Round 4 P4 P4 Round 3 Round 3 P3 P3 Round 2 Round 2 P2 P2 Round 1 Round 1 P1 P1 Slots Slots Supply Aggregate Demand Supply Aggregate Demand Single Product Clock Auction – Intra-Round Bidding Single Product Clock Auction – Intra-Round Bidding Price Price Round 6 Round 6 Round 6 P6 P6 Round 5 Round 5 P5 P5 Round 4 Round 4 P4 P4 Round 3 Round 3 P3 P3 Round 5 Round 2 Round 2 P2 P2 Round 1 Round 1 P1 P1 Slots Slots quantity bid by an individual quantity bid by an individual Single Product Clock Auction – Aggregate Single Product Clock Auction: Activity Rule Demand with Intra-Round Bidding Price Minimal Overshoot Activity rules Round 6 P6 Closing Price Round 5 The problem is that of a bidder hiding as a “snake P5 Round 4 in the grass” until near the end of the auction, to P4 conceal its true interests / values from opponents Round 3 P3 Round 2 Example / evidence: “bid-sniping” in eBay P2 (auction lasts a week, but all meaningful bids Round 1 P1 occur in the last five minutes) Slots Supply Aggregate Demand Single Product Clock Auction: Activity Rule: Quantity Bid at Higher Price ≤ Quantity at Lower Price II: Multi-Product Price Round 6 P6 Round 5 Clock Auctions P5 Round 4 P4 Round 3 P3 Round 2 P2 Round 1 P1 Slots quantity bid by an individual Multi-Product Clock Auction – Closing Multi-Product Clock Auction – Closing 0800 Slot 0900 Slot 0800 Slot 0900 Slot Price Price Price Price P6 XXP5 P’5 XXP5 P’5 P* P* P5P’6 P’5 P4 P’4 P4 P’4 Supply Slots Supply Slots Supply Slots Supply Slots Aggregate demand Aggregate demand Aggregate demand Aggregate demand Multi-Product Clock Auction – Price Points Multi-Product Clock Auction – Price Points Price-Point: Price-point: Price-point: Time Period Start of Round End of Round Time Period Start of Round End of Round 40 % 40%% 75 0600 $ 50 4 slots $ 90 3 slots $150 3 slots 0600 $ 50 4 slots $ 90 3 slots $125 2 slots $150 23 slots 0700 $100 4 slots $160 2 slots $250 2 slots 0700 $100 4 slots $160 2 slots $212.50 2 slots $250 2 slots 0800 $100 6 slots $160 4 slots $250 4 slots 0800 $100 6 slots $160 4 slots $212.50 4 slots $250 4 slots 0900 $100 4 slots $160 4 slots $250 4 slots 0900 $100 4 slots $160 4 slots $212.50 3 slots $250 34 slots 1000 $ 50 4 slots $ 90 3 slots $150 3 slots 1000 $ 50 4 slots $ 90 3 slots $125 3 slots $150 3 slots 1100 $ 50 3 slots $ 90 3 slots $150 3 slots 1100 $ 50 3 slots $ 90 3 slots $125 3 slots $150 3 slots 150 Slots Step Function Meaning of a Bid Step Function Meaning of a Bid Price-point: Price-point: Price-point: Time Period Start of Round End of Round Time Period Start of Round End of Round 40 % 40%% 75 0600 $ 50 4 slots $ 90 3 slots $150 3 slots 0600 $ 50 4 slots $ 90 3 slots $125 2 slots $150 252 slotsSlots 0600 time period 0600 time period Price Price $ 150 $150 $125 $ 90 $ 90 $ 50 $ 50 slots slots 3 4 2 3 4 Maintaining the Quantities from Previous Round Multi-Product Clock Auction – RP Activity Rule Price-point: Time Period Start of Round End of Round 100 % Would like an activity rule (for same reasons as in a single-product clock auction) 0600 $ 50 4 slots $150 4 slots $150 4 slots But simple monotonicity rule is inappropriate, as 0600 time period bidders may want to substitute from one product Price to another $150 Quantities for given products should be weighted by the prices of the respective products, in the correct way $ 50 slots 4 Revealed Preference Activity Rule (RPA) Revealed Preference Activity Rule (RPA) Example of bidding permitted under Revealed Example of bidding not permitted under Revealed Preference Activity Rule: Preference Activity Rule: Time Period Price p1 Quantity q1 Price p2 Quantity q2 Time Period Price p1 Quantity q1 Price p2 Quantity q2 0700 $120,000 8 slots $150,000 8 slots 0700 $120,000 8 slots $150,000 8 slots 0800 $120,000 8 slots $150,000 6 slots 0800 $120,000 8 slots $150,000 10 slots 0900 $100,000 4 slots $110,000 6 slots 0900 $100,000 4 slots $110,000 2 slots The 0700 and 0800 slots became relatively more expensive than The 0700 and 0800 slots again became relatively more the 0900 slots, so it makes sense for the participant to engage expensive than the 0900 slots, yet the participant responded by in substitution from 0700 or 0800 slots into 0900 slots attempting to substitute from the relatively cheaper 0900 slots into the relatively more expensive 0800 slots Revealed Preference Activity Rule (RPA) Revealed Preference Activity Rule (RPA) Any new bid that a bidder attempts to place at time Example of bidding permitted under Revealed t must satisfy the RPA rule with respect to all its Preference Activity Rule: existing bids at times s: Time Period Price p1 Quantity q1 Price p2 Quantity q2 ()RPA ( p−⋅≤−⋅ p ) q ( p p ) q tst tss 0700 $120,000 8 slots $150,000 8 slots If the bidder is bidding according to any consistent 0800 $120,000 8 slots $150,000 6 slots set of valuations, then the RPA rule should never prevent a bidder from placing its desired bid 0900 $100,000 4 slots $110,000 6 slots The web-based auction software enforces a relaxed version of the revealed-preference activity rule — Satisfies (RPA) since: for details, see “Backup Material on RPA Rule” (30,000 × 8) + (30,000 × 6) + (10,000 × 6) ≤ ≤ (30,000 × 8) + (30,000 × 8) + (10,000 × 4) Revealed Preference Activity Rule (RPA) Backup Material on RPA Rule Example of bidding not permitted under Revealed Derivation: Preference Activity Rule: Based on standard analysis in consumer theory. Time Period Price p1 Quantity q1 Price p2 Quantity q2 Consider two times, s and t. Let the associated 0700 $120,000 8 slots $150,000 8 slots prices be ps, pt and let the associated demands be qs , qt . Let v(qs) denote the bidder’s value for qs and 0800 $120,000 8 slots $150,000 10 slots let v(qt) denote the bidder’s value for qt . Note: vq()−⋅≥ p q vq () −⋅ p q 0900 $100,000 4 slots $110,000 2 slots ssstst and: vq()tttsts−⋅≥ p q vq () −⋅ p q . Violates (RPA) since: Adding the inequalities yields the RPA rule: (30,000 × 8) + (30,000 × 10) + (10,000 × 2) > > (30,000 × 8) + (30,000 × 8) + (10,000 × 4) ()RPA ()(). ptst−⋅≤−⋅ p q p tss p q Backup Material on RPA Rule It is often helpful to relax the (RPA) rule. Case 1: () ppq tss −⋅ is positive. The new bid qt is said to satisfy the relaxed revealed preference activity rule if: Mechanics of Mock Auction (((RPA+ ))),for1.