A Combinatorial Auction Designed for the Federal Communications Commission Charles R. Plott California Institute of Technology
BINARY CONFLICT MECHANSMS (BICAP) Winning packages cannot intersect. Binary conflict is a very general concept. Non intersecting paths and routes can be viewed as applications.
TIME PATH OF AUCTION PROCESS SEALED BID THEN CONTINUOUS
Eligibility Forces Bidding: Rules and Management Eligibility t = min [ Activity t-1, Eligibility t-1] max Activity in sealed bid phase Activity in continuous phase S EXPOSURE ³ Eligibility bidding units on item j LIMITS CONSTRAINT all items j bid as singleton S S POSITIONING ³ Eligibility bidding units on item j INCENTIVES CONSTRAINT Î all bids j K K with two or more items
SPEED PARAMETERS INCREMENT REQUIREMENTS - A BID WHEN PLACED MUST BE X% ABOVE THE MAXIMUM COVER b ACTIVITY = WINNING BIDS BIDDING POINTS AGGRESSIVE BIDS 1 + COUNT FOR MORE b WINNING LEVEL BIDS ACTIVITY 2 + b AT OR ABOVE MAXIMUM COVER 3 + b BELOW MAXIMUM COVER 4 The cover of a set K is the maximum of bids in the systems with union contained in K. A bid is dominated if it is less than the value of the cover. For simplicity, a cover limited to unions of singles has been suggested for 3 and 4.
MEASUREMENTS HERE ROUND t END ROUND t+1 END ABC 100 WINNERS ABCD 100 D 15 In ROUND t+2 these two bids will get no activity credit because they are both below their respective covers. The covers for activity are relative to bids in the system when the round opens (in this case bids at the end of one round and bids at the beginning of the next round are the same). BC 20 ABOVE MIN WIN ABCD 100 AD 85 A 40 B 5 BCD 50 ABOVE VALUE OF SINGLES/COVER C 10 BC 20 D 15 A40 B 10 C10 BELOW B 5
Query Results All bids in system. Provisional winners (yellow)
Bids kicked out as provisional winners. Bids brought in as provisional winners.
DOES IT WORK? Proof of Concept: Efficiency Design Consistency: ?
A B C D E F G H I J K L A B C D E F G H I J K L The colors represent bidders and not whether a package is involved. first best 100% efficiency Actual outcome at 98% efficiency. The inefficiency is due to misallocations of the second six items, which are of low value. Only I and K are in the wrong hands.
Efficient allocation and actual allocation in the 34 license experiment. Color of box is bidder who should get the license. The dot is the color of the bidder who got the license. No dot on a license means the right bidder got it. Notice that the pattern is complex. All bidders have a preference for all licenses. Efficiency forces compromises as shown.