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The Clock-Proxy Auction: A Practical Combinatorial Auction Design

The Clock-Proxy Auction: A Practical Combinatorial Auction Design. Lawrence M. Ausubel, Peter Cramton, Paul Milgrom University of Maryland and Stanford University 8 October 2004. * Some of the methods discussed are subject to issued patents or pending applications. Introduction.

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The Clock-Proxy Auction: A Practical Combinatorial Auction Design

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  1. The Clock-Proxy Auction:A Practical Combinatorial Auction Design Lawrence M. Ausubel, Peter Cramton, Paul Milgrom University of Maryland and Stanford University 8 October 2004 * Some ofthe methods discussed are subject to issued patents or pending applications.

  2. Introduction • Many related (divisible) goods • Spectrum (location) • Electricity (duration, location, strike price, ancillary services) • Financial securities (duration) • Emissions (duration, type) • A practical combinatorial auction for FCC (and others) to replace simultaneous ascending auction (SAA)

  3. Introduction Clock Auction • Auctioneer names prices; bidders name only quantities • Price adjusted according to excess demand • Process repeated until market clears • No exposure problem (package auction)

  4. Introduction Proxy Auction • A procedure for package bidding • Bidders input their values into “proxy agents” • Proxy agents iteratively submit package bids, selecting best profit opportunity according to the inputted values • Auctioneer selects provisionally-winning bids according to revenue maximization • Process continues until the proxy agents have no new bids to submit

  5. Introduction Clock-Proxy Auction • A clock auction, followed by a “final round” consisting of a proxy auction • Bidders directly submit bids in clock auction phase • When clock phase concludes, bidders have a single opportunity to input proxy values • The proxy phase concludes the auction

  6. Introduction Clock-Proxy Auction • All bids are kept “live” throughout auction (no bid withdrawals) • Bids from clock phase are also treated as package bids in the proxy phase • All bids are treated as mutually exclusive (XOR) • Activity rules are maintained within clock phase and between clock and proxy phases

  7. Introduction Advantages of Clock-Proxy Auction • Clock phase • Simple for bidders • Provides essential price discovery • Proxy phase • Highly efficient • Competitive revenues • Little opportunity for collusion

  8. Clock Auction

  9. Simultaneous Clock Auction • Practical implementation of the fictitious “Walrasian auctioneer” • Auctioneer announces a price vector • Bidders respond by reporting quantity vectors • Price is adjusted according to excess demand • Process is repeated until the market clears

  10. Simultaneous Clock Auction • Strengths • Simple for bidders • Provides highly-usable price discovery • Yields similar outcome as SAA, but faster and fewer collusive opportunities • A package auction without complexity • Weaknesses • Limits prices to being linear • Therefore should not yield efficient outcomes

  11. Recent Clock Auctions (MDI) • EDF generation capacity (virtual power plants) • 13 quarterly auctions (Sep 2001 – present) • Electrabel generation (virtual power plants) • 4 quarterly auctions (Dec 2003 – present) • Ruhrgas gas release program • 2 annual auctions (2003 – present) • UK emissions trading scheme • World’s first greenhouse gas auction (Mar 2002) • GDF and Total gas release program • 2 auctions (Oct 2004) • FirstEnergy (Ohio) standard offer service • 1 annual auction (Nov 2004)

  12. Recent Clock Auctions (others) • New Jersey basic generation service • 3 annual auctions (2002 – present) • Texas electricity capacity • 12 quarterly auctions (Sep 2001 – present) • Austrian gas release program • 2 Annual Auctions (2003 – present) • Nuon generation capacity • One auction (July 2004)

  13. EDF Generation Capacity Auction MDI market design inc.

  14. Typical EDF Auction • Number of products • Two to five groups (baseload, peakload, etc.) • 20 products (various durations) • Number of bidders • 30 bidders • 15 winners • Duration • Eight to ten rounds (one day) • €200 million in value transacted in auction

  15. Electrabel VPP Capacity Auction MDI market design inc.

  16. Typical Electrabel Auction • Number of products • Two groups (baseload, peakload) • 20 products (various durations and start dates) • Number of bidders • 14 bidders • 7 winners • Duration • Seven rounds (one day) • €70 million in value transacted in auction

  17. Typical Ruhrgas Auction • Number of products • One (39 identical lots) • Number of bidders • 16 bidders • 7 winners • Duration: part of one day • €350 million in value transacted in auction

  18. Issues in Implementing Clock Auction • Bids need to be taken literally and need to be treated as binding contractual offers • PROBLEM: If bids need to be submitted unreasonably frequently or at unexpected intervals, bidders may miss making required submissions of bids • SOLUTION: Discrete bidding rounds • Avoiding “overshoot” • PROBLEM: Given discrete bidding rounds and need for a quick auction, bid increments need to be reasonably large, and price may overshoot the market-clearing price • SOLUTION: Intra-round bidding

  19. Round 6 P6 Closing Price: 1 Product – Dealing with Discreteness Price Overshoot Round 5 P5 Round 4 P4 Round 3 P3 Round 2 P2 Round 1 P1 MW Aggregate Demand Supply

  20. Round 6 Round 6 P6 Round 5 P5 Round 4 P4 Round 3 P3 Round 5 Round 2 P2 Round 1 P1 1 Product introducing intra-round bidding Price MW quantity bid by an individual

  21. Round 6 P6 Round 5 P5 Round 4 P4 Round 3 P3 Round 2 P2 Round 1 P1 1 product – Individual bids with intra-round bidding Price MW quantity bid by an individual

  22. Minimal Overshoot Round 6 P6 Closing Price Round 5 P5 Round 4 P4 Round 3 P3 Round 2 P2 Round 1 P1 1 product – Aggregate demand with intra-round bidding Price MW Aggregate Demand Supply

  23. Sample 1

  24. Sample 2

  25. Simultaneous Clock Auction Issue 2: Treatment of bids which would make aggregate demand < supply • Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce its demand • Naive approach: Prevent the reduction • Example: For a particular item, demand > supply, but demand < supply at next increment • Naive approach: Ration the bidders

  26. Simultaneous Clock Auction Issue 2: Treatment of bids which would make aggregate demand < supply • Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce its demand • Difficulty: Creates an exposure problem • Example: For a particular item, demand > supply, but demand < supply at next increment • Difficulty: Creates an exposure problem

  27. Simultaneous Clock Auction Issue 2: Treatment of bids which would make aggregate demand < supply • Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce its demand • Our approach: Allow the reduction • Example: For a particular item, demand > supply, but demand < supply at next increment • Our approach: No rationing

  28. Simultaneous Clock Auction Issue 2: Treatment of bids which would make aggregate demand < supply • “Full Flexibility” (used in the EDF auctions; advocated here) • After each new price vector, bidders can arbitrarily reduce their previous quantities • Advantage • Makes clock auction into a combinatorial auction • No exposure problem! • Disadvantage • There may be significant undersell • Not a problem if it is followed by a proxy auction

  29. Simultaneous Clock Auction Issue 3: Activity rules • Prevent a bidder from hiding as a “snake in the grass” to conceal its true interests • Standard approaches: • No activity rule (laboratory experiments) • Monotonicity in quantities (SAA and clock auctions in practice)

  30. Simultaneous Clock Auction Issue 3: Activity rules • Revealed-preference activity rule (advocated here) • Compare times s and t (s < t), Prices: ps, ptDemands: xs, xt • At time s, xs is better than xt: • At time t, xt is better than xs : • Adding inequalities yields the RP activity rule:

  31. Simultaneous Clock Auction Issue 3: Activity rules • Revealed-preference activity rule (advocated here) • Bid placed at time t must satisfy (RP) with respect to its prior bids at all prior times s (s < t): • One can also apply a “relaxed” RP in proxy phase (with respect to bids in the clock phase)

  32. Proxy Auction

  33. Package Bidding • Package bidding often motivated by complements • Even without complements, package bidding may improve outcome by eliminating “demand reduction” • In SAA, bidders may have strong incentives to reduce demands in order to end auction at low prices

  34. Basic Ascending Package Auction • A set of items is offered for sale • A bid specifies a set of items and a corresponding bid amount • Bidding proceeds in a series of rounds • After each round, provisional winning bids are determined that maximize revenues • Auction ends after a round with no new bids • All bids are treated as mutually exclusive (XOR) • All bids are kept “live” throughout the auction

  35. Ascending Proxy Auction • Each bidder reports its values (and constraints) to a “proxy bidder” • Proxy bidder bids on behalf of the real bidder — iteratively submitting the allowable bid that, if accepted, would maximize the bidder’s payoff (evaluated according to its reported values) • Auction ends after a round with no new bids

  36. Example: Ascending Proxy Auction • Two items, A and B; bids must be integers • Bidder reports values of v(A) = 10, v(B) = 5, v(A,B) = 20 • Past high bids by this bidder (all “losing”) were: • b(A) = 4, b(B) = 3, b(A,B) = 15 • Next allowable bids are: • b(A) = 5 Yields profits of  = v(A) – b(A) = 10 – 5 = 5 • b(B) = 4 Yields profits of  = v(B) – b(B) = 5 – 4 = 1 • b(A,B) = 16 Yields profits of  = v(A,B) – b(A,B) = 20 – 16 = 4 • So the proxy bidder next places a bid of 5 on A

  37. Example: Ascending Proxy Auction • Two items, A and B; bids must be integers • Bidder reports values of v(A) = 10, v(B) = 5, v(A,B) = 20 • Past high bids by this bidder (all “losing”) were: • b(A) = 4, b(B) = 3, b(A,B) = 15 • Next allowable bids are: • b(A) = 5 Yields profits of  = v(A) – b(A) = 10 – 5 = 5 • b(B) = 4 Yields profits of  = v(B) – b(B) = 5 – 4 = 1 • b(A,B) = 16 Yields profits of  = v(A,B) – b(A,B) = 20 – 16 = 4 • Next allowable bids after that are: • b(A) = 6 Yields profits of  = v(A) – b(A) = 10 – 6 = 4 • b(B) = 4 Yields profits of  = v(B) – b(B) = 5 – 4 = 1 • b(A,B) = 16 Yields profits of  = v(A,B) – b(A,B) = 20 – 16 = 4 • So the proxy next bids 6 on A and/or 16 on {A,B}

  38. Outcomes in the Core • The coalitional form game is (L,w), where… • L denotes the set of players. • the seller is l = 0 • the other players are the bidders • w(S) denotes the value of coalition S: • If S excludes the seller, let w(S)=0 • If S includes the seller, let • The Core(L,w) is the set of all profit allocations that are feasible for the coalition of the whole and cannot be blocked by any coalition S

  39. Outcomes in the Core Theorem. (Ausubel and Milgrom 2002 , Parkes and Ungar 2000) The payoff vector resulting from the proxy auction is in the core relative to the reported preferences Interpretations: • Core outcome assures competitive revenues for seller • Core outcome assures allocative efficiency (ascending proxy auction is not subject to inefficient demand reduction)

  40. Case of Substitutes • If goods are substitutes, then Vickrey payoff profile is bidder-Pareto-optimal point in core • Outcome of the ascending proxy auction coincides with outcome of the Vickrey auction Vickrey Payoff Vector w(L)-w(L\2) Core Payoffs for 1 and 2 Bidder #2 Payoff v1+v2w(L)-w(L\12) Bidder #1 Payoff w(L)-w(L\1)

  41. Case of Non-Substitutes • If goods are not substitutes, then Vickrey payoff profile is not in core • Ascending proxy auction yields a different outcome from the Vickrey auction (one with higher revenues) Vickrey Payoff Vector w(L)-w(L\2) Bidder-Pareto-optimal payoffs Core Payoffs for 1 and 2 Bidder #2 Payoff v1+v2w(L)-w(L\12) Bidder #1 Payoff w(L)-w(L\1)

  42. Outcomes in the Core Theorem (Ausubel and Milgrom 2002). If  is a bidder-Pareto-optimal point in Core(L,w), then there exists a full information Nash equilibrium of the proxy auction with associated payoff vector . These equilibria may be obtained using strategies of the form: bid your true value minus a nonnegative constant on every package

  43. Proxy Auction Avoids Vickrey Problems • In Vickrey auction: • Adding a bidder can reduce revenues • Using a shill bidder can be profitable • Losing bidders can profitably collude

  44. Monotonicity and Revenue Issues • Example: Two identical items, A and B; three bidders • Bidder 1 values the pair only: v1(A,B) = $2 billion • Bidder 2 wants a single item only: v2(A) = $2 billion • Bidder 3 wants a single item only: v3(B) = $2 billion • The Vickrey auction awards each bidder his incremental value: • Bidders 2 and 3 each win one item • Social value with Bidder 2 = $4 billion; without Bidder 2 = $2 billion • Prices in the Vickrey auction equal zero! • The problem in this example is a failure of monotonicity: • Adding Bidder 3 reduces Vickrey revenues from $2 billion to zero • The Vickrey outcome lies outside the core • The proxy auction avoids this problem: Revenues = $2 billion

  45. The Loser Collusion Problem • Example: Two identical items, A and B; three bidders • Bidder 1 values the pair only: v1(A,B) = $2 billion • Bidder 2 wants a single item only: v2(A) = $0.5 billion • Bidder 3 wants a single item only: v3(B) = $0.5 billion • The losing Bidders 2 and 3 have a profitable joint deviation in the Vickrey auction: bidding $2 billion each • This converts it into the previous example • Bidders 2 and 3 each win one item at prices of zero • The Vickrey auction is unique in its vulnerability to collusion even among losing bidders • The proxy auction avoids this problem: Bidders 2 and 3 can overturn the outcome of Bidder 1 winning only by jointly bidding $2 billion

  46. The Shill Bidding Problem • Example: Two identical items, A and B; two bidders • Bidder 1 values the pair only: v1(A,B) = $2 billion • Bidder 2 has v2(A) = $0.5 billion; v2(A,B) = $1 billion • The losing Bidder 2 can set up a bidder under a false name (“shill bidder”). Each of Bidder 2 and the shill Bidder 3 can bid $2 billion each • This again converts it into the first example • Bidder 2 wins two items and pays zero! • The Vickrey auction is vulnerable to shill bidding

  47. Clock-Proxy Auction

  48. Clock-Proxy Auction • A simultaneous clock auction is conducted, with a revealed-preference activity rule imposed on bidders, until (approximate) clearing is attained • A proxy auction is conducted as a “final round” • Bids submitted by proxy agents are restricted to satisfy a relaxed revealed-preference activity rule based on competitive conditions • Bids from clock phase are also treated as “live” package bids in proxy phase • All package bids (clock and proxy) are treated as mutually exclusive, and auctioneer selects as provisionally-winning the bids that maximize revenues

  49. Relaxed Revealed Preference Activity Rule • Let s be a time in clock phase and t a time in proxy phase • Package S is bid on at time s and T is bid on at time t • Ps(S) and Ps(T) package prices of S and T at time s • Pt(S) and Pt(T) package prices of S and T at time t • At every time t in the proxy phase, the bidder can bid on the package T only if (RRP) is satisfied for every package S bid at time s in the clock phase • (RRP) [Pt(S) – Ps(S)] Pt(T) – Ps(T) •  > 1 is parameter (closer to 1 if more competitive environment) • For  = 1, price of S increased more than price of T; otherwise S would be more profitable than T. • Alternatively, state RRP as a constrain on valuations reported to proxy:

  50. Why Not Use the Proxy Auction Only? • Clock auction phase yields price discovery • Feedback of linear prices is extremely useful to bidders • Clock phase makes bidding in the proxy phase vastly simpler • Focus decision on what is relevant • See what you don't need to consider • See what looks like good possibilities

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