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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.

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

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

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

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

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

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

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Clock Auction

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

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

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

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

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EDF Generation Capacity Auction MDI market design inc.

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

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Electrabel VPP Capacity Auction MDI market design inc.

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

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

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Issues in Implementing Clock Auction n Bids need to be taken literally and need to be treated as binding contractual offers u PROBLEM: If bids need to be submitted unreasonably frequently or at unexpected intervals, bidders may miss making required submissions of bids u SOLUTION: Discrete bidding rounds n Avoiding “overshoot” u 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 u SOLUTION: Intra-round bidding

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

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

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

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

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Sample 1

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Sample 2

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

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

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

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

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

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Issue 3: Activity rules n Revealed-preference activity rule (advocated here) n Compare times s and t (s < t), Prices: p s, p t Demands: x s, x t u At time s, x s is better than x t : u At time t, x t is better than x s : u Adding inequalities yields the RP activity rule: Simultaneous Clock Auction

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

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Proxy Auction

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

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

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Ascending Proxy Auction n Each bidder reports its values (and constraints) to a “proxy bidder” n 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) n Auction ends after a round with no new bids

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

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

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Outcomes in the Core n The coalitional form game is (L,w), where… n L denotes the set of players. u the seller is l = 0 u the other players are the bidders n w(S) denotes the value of coalition S: u If S excludes the seller, let w(S)=0 u If S includes the seller, let n 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

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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: n Core outcome assures competitive revenues for seller n Core outcome assures allocative efficiency (ascending proxy auction is not subject to inefficient demand reduction)

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

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

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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

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

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

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

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The Shill Bidding Problem n Example: Two identical items, A and B; two bidders u Bidder 1 values the pair only: v 1 (A,B) = $2 billion u Bidder 2 has v 2 (A) = $0.5 billion; v 2 (A,B) = $1 billion n 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 u This again converts it into the first example u Bidder 2 wins two items and pays zero! n The Vickrey auction is vulnerable to shill bidding

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Clock-Proxy Auction

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

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Relaxed Revealed Preference Activity Rule n Let s be a time in clock phase and t a time in proxy phase n Package S is bid on at time s and T is bid on at time t n P s (S) and P s (T) package prices of S and T at time s n P t (S) and P t (T) package prices of S and T at time t n 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 n (RRP) [P t (S) – P s (S)] P t (T) – P s (T) n > 1 is parameter (closer to 1 if more competitive environment) n For = 1, price of S increased more than price of T; otherwise S would be more profitable than T. n Alternatively, state RRP as a constrain on valuations reported to proxy:

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

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n Proxy auction ends with core outcome u Efficient allocation u Competitive revenues n No demand reduction n Collusion is limited u Relaxed activity rule means allocation still up for grabs in proxy phase Why Not Use the Clock Auction Only?

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n Clock auction is a fast and simple process (compared to the simultaneous ascending auction) u Only provide information relevant for price and quantity discovery (excess demand) u Takes advantage of substitutes (one clock for substitute licenses) u Example: – proposed 90 MHz of 3G spectrum in 5 blocks: 30, 20, 20, 10, 10 – clock alternative: 9 or 18 equivalent blocks per region u Fewer rounds – Get increment increase for all items, rather than having to cycle through over many rounds – “Intra-round bids” allow larger increments, but still permit expression of demands along line segment from start-of-round price to end-of-round price Advantages of the Clock over the SAA

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n Clock auction limits collusion (compared to the simultaneous ascending auction) u Signaling how to split up the licenses greatly limited – No retaliation (since no bidder-specific information) – No stopping when obvious split is reached (since no bidder specific information) u Fewer rounds to coordinate on a split Advantages of the Clock over the SAA

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n No exposure problem (unlike SAA) u As long as at least one price increases, bidder can drop quantity on other items u Bidder can safely bid for synergistic gains u Bid is binding only as full package n No threshold problem (unlike ascending package auction) u Clocks controlled by auctioneer: no jump bids; large bidder cannot get ahead u Linear pricing: small bidders just need to meet price on single item Advantages of the Clock Phase

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n Combines advantages of u Clock auction u Proxy auction n Excellent price discovery in clock phase simplifies bidder decision problem n Proxy phase enables bidders to fine-tune allocation based on good price information Clock-Proxy Auction

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Advantages of Clock-Proxy Auction n Clock u Take linear prices as far as they will go u Simplicity and flexibility for bidders and auctioneer u Expand substitution possibilities u Minimize scope for collusion u No exposure problem; no threshold problem n Proxy u Core outcome – Efficiency – Substantial seller revenues

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